Blues' had a goal disallowed late on as they had to settle for a share of the spoils.BCFC
Lee Camp saved Paddy McNair's penalty before Lukas Jutkiewicz powered Blues into a 27th minute lead with a trademark header.
Blues from then on controlled proceedings and could and should have put matters to bed; Kerim Mrabti struck the post and Blues fashioning plenty of good openings in the second-half.
But with nine minutes left Ashley Fletcher equalised and then matters erupted when Blues thought Jutkiewicz had scored again.
But referee Andy Woolmer halted play - with Blues on a dangerous counter attack and in on the left of Boro's area - for an apparent head injury to Marcus Tavernier, some 60 yards back downfield.
Blues protested as Boro's medical staff 'stormed' the pitch in-play to draw attention to Tavernier flat out on the deck, said Pep Clotet, and it sparked a ruck between coaches and backroom staff from both teams that saw Sean Rush receive a red card.
Rush took exception to Leo Percovich trying to remonstrate with Clotet, who was unhappy at what had unfolded, and the Boro goalkeeper coach was also sent-off after the fracas around the technical area, that also brought players rushing from the pitch to join in.
Tavernier, as it happened, was fine to carry on looking none the worse for wear after seemingly appearing motionless after being in collision with Jude Bellingham and losing possession. Blues understandably felt aggrieved that their goal had been chalked off.
During a quiet opening 15 minutes Jeremie Bela had the game's first two shots at goal, the first dragged just wide of the front post after a long throw by Marc Roberts and the second straight at Aynsley Pears following a nicely worked move by Blues, started at right-back by Maxime Colin.
Otherwise it had been a steady start to proceedings with Blues staying organised and true to their shape to keep the hosts well away from danger.
But, in the 23rd minute, from Boro's first real attack of purpose, they earned a penalty.
The ball was played into the right of the box for Lukas Nmecha, who backheeled it into the path of Patrick Roberts, who could angle in on goal.
Gary Gardner came across and stuck his leg out to try and half him and only succeeded in hampering his stride, Roberts stumbled.
The referee pointed to the spot and McNair took responsibility from 12 yards.
McNair struck it true and hard, but Camp was equal to it, diving to the right of his goal to beat it away with both hands - wonderful save.
Four minutes later Blues made it a double whammy for Boro by going ahead.
Bela did some nice work wide on the right before lifting in a cross perfectly towards the far stick - and there was Jutkiewicz, rising above Jonny Howson, to power in an unstoppable header into the roof of the net.
After that flourish activity - and a key sliding block by Roberts to stop Fletcher getting a shot on target from a great position - Blues managed to settle things down again to their liking.
And, in the 34th minute, they could have gone further ahead.
Gardner intercepted a pass in Boro's half, and ran on to accept Mrabti's return pass, that was delivered overhead.
Gardner centred low towards Jutkiewicz and Pears just about got the ball away, lunging low with his hands to divert it from the striker's feet.
It came back out to Mrabti on the edge of the box and he chopped by Lewis Wing before planting a low left-footer that hit the post with Pears beaten but stayed out - so close.
Moments later Boro had to make their second substitution of the half due to injury, Dael Fry joining Roberts - who went off just after the penalty - on the treatment table.
Blues gave Boro a couple more scares before the interval, with Bela and Mrabti both almost capitalising in the heart of the area as the visitors continued to stretch the defensive limits.
The home team responded with a 25-yarder by Nmecha that took one bounce as it flashed past Camp's left-hand post.
But overall it was a very thorough job done by Blues in the half, Camp providing initial inspiration with the penalty save.
Jutkiewicz's goal - his 10th of the season - was the first Blues have scored at the Riverside in five visits.
Half-time: Boro 0 Blues 1
Boro were sent out a good few minutes early for the second half, presumably having had an ear bashing at the break from Jonathan Woodgate.
There was certainly more urgency about Boro in the opening exchanges, but Blues remained defensively calm but alert.
And in the 59th minute, after a short free-kick, Blues worked a nice angle for Bela to deliver an inswinging cross for Kristian Pedersen, who had stayed in the box. He got a looping header in and the ball had Pears scrambling as it dropped just over the bar onto the roof of the net.
Blues first change came just after the hour with Mrabti's energetic and eager performance ending, Dan Crowley entering the fray to inject more impetus in the 10 role.
And he almost had an immediate impact, lifting a brilliant pass into the path of Roberts, who was up from a free-kick that Blues weaved forward from their own half.
Unfortunately Roberts got the ball stuck under his feet somewhat and the chance to get a shot away from a great position subsided.
By this stage, with Boro fans increasingly restless, Blues looked the more likely to score again.
But, as ever, football can change in the blink of an eye. Boro won a corner, brought on their third and final substitute - Rudy Gestede - and he promptly charged in to the flag kick and put a header just over.
Blues came back at Boro and Crowley set Jacques Maghoma up on the left of the area and his precise sidefooter dribbled wide of the post. Then Gardner strode forward into a great position, 25 yards out, and thumped a controlled shot that Pears kept out only with a full-length dive.
Gardner then powered all the way through again and only Djed Spence taking the ball off his toes at the last minute, getting it back to the 'keeper, stopped him scoring.
Blues could have put things to bed in that little spell as Boro were struggling to cope.
David Davis - again excellent in tandem with Gardner - appealed in vain for a penalty when Wing bumped right into him carelessly as he tried to readjust in the heart of the area as Crowley and Maghoma knitted together a crisp couple of passes to create an opening once more.
From a counter, led by substitute Bellingham, Crowley picked out Jutkiewicz at the far post and his downward header was hastily cleared over the crossbar by Howson facing his own goal. Blues continued to fashion openings to make things safe - Juke then heading the corner straight at the 'keeper, as we moved into the final 10 minutes.
Those chances that weren't converted came home to roost as Boro equalised, through Fletcher.
Boro got the ball out to the left flank, after it sailed over from a cross on the right. Marvin Johnson thumped it low towards the six-yard box. Fletcher managed to get to it just before Roberts, coming around from behind him, and a deft flick sent it skidding past Camp.
All the good work, the good play up to then counted for nothing as a revitalised Boro then staged a late flourish to the finish.
There was the huge controversy in the 87th minute when Blues scored seconds after referee Woolmer stopped play as a cross came in from the left of the Boro area, from Bellingham.
Boro players had signalled for him to halt proceedings as Tavernier ran into Bellingham's arm and was struck on the chin, deep in the Blues half. Tavernier stayed down, flat out.
Woolmer, who was yards from the incident, allowed play to continue. Pedersen won the ball and Blues surged forward, through Bellingham.
He switched play to the left and Crowley, got the ball back and Bellingham's cross was touched on again by Maghoma and Jutkiewicz steered it home - but the referee had turned his back and was running the other way, clearly influenced by a hullabaloo that had centred around Tavernier.
Blues were absolutely furious. Both benches cleared, a scuffle broke out and when calm was restored the two red cards were brandished and Clotet received yellow.
Blues still could not believe it as they had a goal chalked off, Tavernier came back on - he sprang back up to his feet when a stretcher came for him - and a sense of injustice raged.
In the second minute of added-time, from Roberts long throw, a scramble in the Boro box ensued and a clearance cannoned off Jutkiewicz and went agonisingly over the crossbar.
Blues attacked again, forced another corner and remarkably, Boro broke, three on three, and forced a corner of their own - which Camp came and caught.
Blues then went down the other end and threatened again and eventually the frenetic finale came to a halt with everyone trying to catch their breath and work out what on earth had happened - and just who was in the right or wrong.
Boro (3-5-2): Pears, Spence, Howson, Fry (Wood 36), McNair, Johnson, Saville (Gestede 67), Wing, Roberts (Tavernier 25), Nmecha, Fletcher. Subs not used: Mejias, Clayton, Reading, Liddle.
Goal: Fletcher (81)
Sent off: Leo Percovich (87)
Blues (4-2-3-1): Camp, Colin, Pedersen, Roberts, Clarke-Salter, Davis, Gary Gardner, Bela (Bellingham 76), Mrabti (Crowley 61), Maghoma, Jutkiewicz. Subs not used: Montero, McEachran, Gimenez, Trueman, Sunjic.
Goal: Jutkiewicz (27)
Booked: Gardner (35), Clotet (88)
Sent off: Sean Rush (87)
Referee: A Woolmer
Attendance: 18,350 (355 away)