They trailed by three goals after 26 minutes and could have been further behind.
But two goals in two second-half minutes, from Miguel Fernandez and Adan George from the penalty spot, put the outcome in doubt, and more likely in Blues favour.
But Forest managed to hang in there and see the game out, thus moving ahead of Blues in the standings on goal difference, with the teams level on 27 points.
Gary Gardner got 73 minutes in the tank on his return to action from injury and David Stockdale also figured, and kept Blues in it with two excellent saves early on.
Forest were aggressive, lively and pressed very, very well from the off and that put Blues off kilter.
After three minutes, after Ryan Burke gave the ball away to Kieth Asare, Forest should have gone ahead but Alex Mighten stuck the subsequent wide from a great position in the box.
Then, after Mighten drove forward with the ball after a Ryan Stirk tackle (in which he took a whack and had to be replaced at the interval), he played in Asare and Stockdale made a good stop with the body, from the low shot.
From a right wing corner Ethan Stewart powered down a header and Stockdale produced a brilliant save, reacting quickly to get down and his right hand on the attempt, virtually on the line, before it was scrambled away.
Barely seven minutes had gone and Blues were well and truly on the ropes.
Blues first shot came from Caolan Boyd-Munce, who thudded a left-footer into the advertising hoardings just wide, after Kane Thompson-Sommers slithered his way forward and teed him up ourside the area.
But immediately afterwards, in the 13th minute, Blues fell behind. A raking, crossfield pass from the right was taken in his stride on the chest by Mighten, who attacked Ben Forrest down the outside moving into the box before finishing low into the far bottom corner.
The second goal came after 20 minutes when Joe Redmond was dispossessed on halfway and Asare surged on down the left. He crossed low and Kieran Hayes made an excellent diagonal run in support to slide in and toe-end the ball past Stockdale from close range.
It was 3-0 in the 26th minute as Forest got a break, when a ball was played into Asare and he let fire, from a few yards outside the area. His shot cannoned off Redmond and wrong-footed Stockdale.
Blues changed their system from a diamond to 4-2-3-1 to try and gain more control and at least for the remainder of the half they were much more in the game.
After the break, they were a different proposition altogether.
With Thompson-Sommers making a real impact in behind the front and George's speed and mobility more than useful in the wide position of the three, Forest were asked plenty of questions.
Blues shifted the ball a lot better and forward, without hesitation. Burke got in on occasions down the left-hand side, helping to seize the initiative.
In the 53rd minute after Burke and George combined high up, Thompson-Sommers broke into the right of the area and drilled a shot just past the far post.
That was the sign of things to come as in the 57th minute, after Forrest regained the ball for Blues as they put pressure on, George burst forward and squared a cross to the centre of the area where Fernandez took a touch before sidefooting into the bottom corner.
Less than two minutes later Blues had another goal. It came from a fine, defence-splitting pass by Thompson-Sommers, finding Burst breaking into the box. He was bundled over from behind by Stewart and George took the resulting penalty, planting it to the right as the 'keeper went the other way.
Blues were now in the ascendancy and continued to take the game to Forest.
Burke came agonisingly close to a spectacular leveller after using Boyd-Munce's run to his left to distract the defence. He veered past two challenges coming inside before cracking a right-footer from 25 yards that thundered onto the crossbar. The ball came back out to Gardner, who sidefooted home, but he was flagged offside.
Stockdale did well to get his position exact to block a fierce drive by Liam Sole as Blues were almost undone on the counter.
But they kept on pressing to the end as Forest dug in.
Into added-time, and the hosts managed to keep out a dangerous free-kick and two successive corners by Boyd-Munce as the tension levels rocketed; Redmond going very close on the latter delivery as he flew in with his marker to make contact six yards out.
But it was not to be for Blues, who were left to reflect on a first league loss in seven matches and their opponents going top of the division.
Blues: Stockdale, Forrest (Andrews 89), Burke, Redmond, Roberts, Gary Gardner (Reid 73), Stirk (Campbell ht), Boyd-Munce, Thompson-Sommers, Fernandez, George. Sub not used: Gordon.