Blair's second-half tap-in was enough to end York's 17-match unbeaten run, after Saturday's original clash was postponed due to a waterlogged pitch.
There was little between the two promotion hopefuls, but Fleetwood looked the more threatening of the two teams and will head back to Highbury Stadium on Friday night with a deserved one-goal advantage.
Antoni Sarcevic stung the palms of on-loan York keeper Nick Pope on 18 minutes as Fleetwood settled the better of the two teams.
And the hosts also had a a brief scare when David Ball's header down in the penalty area hit the chest of Calvin Andrew and down the arm of the York striker, but referee Carl Boyeson waved away Fleetwood's brief appeals.
Before that Andrew had come close for York but saw his goal-bound shot from Ryan Brobbel's cut back blocked by two Fleetwood defenders.
But Fleetwood continued to have the upper hand and John McCombe was fortunate to see a powerful cross from Ball deflect off him and into the arms of the grateful Pope.
The hosts upped the tempo at the start of the second half and Michael Coulson almost opened the scoring on 48 minutes.
The highly-rated York forward cut in neatly from the left, before hammering a low shot across the six-yard box, which Andrew failed to connect with.
But moments later the visitors were ahead through Blair's close-range strike.
Ball's trickery on the right allowed Sarcevic to fire in a low cross, which Blair converted from inside the six-yard box at the second attempt after his first-time shot was blocked on the line by Lanre Oyebanjo.
And the visitors almost doubled their lead soon after through the lively Ball, but he was denied by Pope with just the keeper to beat.
York upped the ante and threw bodies forward, but almost got caught on the break as Josh Morris played in Iain Hume, but the on-loan Preston forward dragged his shot wide of the target.