Blues spectacular opener came after a 16-pass move from deep in their own half involving every player bar onebcfc.com
After a below par opening period, Blues came out brimming with intent and earned the spoils through a spectacular Caolan Boyd-Munce strike and an Odin Bailey penalty.
And Boyd-Munce's goal was pretty special for more than one reason: it came after Blues somehow passed their way out from a seemingly impossible situation when penned deep in the left-back position, not far from the corner quadrant.
They way they maneuvered the ball and then swept from one side of the pitch to the other brought gasps and applause from those watching in the stands, even before Boyd-Munce let rip with a whipped 25-yarder that flew into the net.
The victory moved Blues back to the head of pile, three points clear of Nottingham Forest.
And it was their sixth in a row in the league, with the clean sheet meaning that they have only conceded one goal in nine hours of PDL football.
Blues were not quite at it in the first-half. They couldn't get their combinations going against a Sheffield side that dropped back from halfway and made space a premium.
A long range attempt from Ryan Burke, Blues most effective player in the first-half, brought out a parrying save from Josh Render.
But Blues did look vulnerable, with Osaze Uroghide's ball over the top sending Conor Grant clean through. Instead of carrying on and shooting, he checked back and tried to beat Moha Ramos with a scooping attempt, which was easily gathered.
Then, after a give and go, Grant found himself facing down Ramos but his execution was wanting and Ramos again cleaned up.
Josh Andrews went near with a flick on a deflected cross, and on the stroke of half-time Jack Concannon tried to shape a shot beyond the 'keeper from the left edge of the area, only for Render to bat it away one-handed.
But it wasn't the usual fare from Blues and Steve Spooner dished out a few home truths during the interval.
From the get-go after the break the difference in Blues was marked. The passing was crisp and quicker, the work rate ratcheted up and the determination to dominate play - and
tighten things up - apparent.
Sheffield managed to keep Blues out until the 64th minute, with the goal coming from Ramos punching clear a dangerous cross, which was retrieved by Bailey, setting in motion and truly wonderful move and goal.
From there Blues kept their cool and composure, passing their way through Sheffield's press - Geraldo Bajrami's deft backfoot, Cruyff-lite touch buying an extra yard in a tight spot a particular highlight - with every player bar Andrews involved by the end.
When it came back over to the left for Boyd-Munce, the Northern Ireland Under-21 international shifted it onto his left peg 25 yards out and hit a searing shot across the 'keeper.
Sixteen passes and sixty seconds later after Ramos' initial intervention - what a goal.
Blues, with confidence searing, proceeded to exact a further stranglehold on the match.
The second goal came in the 72nd minute, from the spot.
Substitute Tate Campbell waltzed past two challenges after taking a Concannon pass and as he readied himself to slot home, he was unceremoniously taken out by a robust challenge from the side by Uroghide.
Bailey took responsibility from 12 yards and slammed the ball down the middle as the 'keeper committed himself to the left.
The penalty award came after another slick passage of play by Blues, who worked Campbell in on the burst following a raking diagonal pass by Joe Redmond and a backheel by Boyd-Munce.
In stoppage-time Blues were unfortunate not to have got a third goal, from a free-kick.
Redmond, as he showed in the previous match, has been honing his hitherto unbeknownst talents from the dead ball and punched a swerving sidefooter past the wall and onto the post; the ball rebound down and across and was spinning over the line before the interventions of a defender, scooping it away. Even then, as Blues regained possession and centred into the box, Campbell was brought crashing to the floor as he tried to cash in, which should have been another penalty.
Blues: Ramos, Forrest, Burke, Stirk, Redmond, Bajrami, Thompson-Sommers (Campbell 61), Boyd-Munce, Andrews (Reid 83), Bailey, Concannon (Baker 89). Subs not used: Roberts, Fernandez.