United's FA Youth Cup dream is over for another season.
Despite taking a first-half lead through Dominic Calvert-Lewin, the Blades surrended their advantage immediately before conceding two goals in a matter of minutes after the restart at Highbury Stadium.
It was the visitors who had the first sight of goal as early as the 5th minute, but home goalkeeper Bleeker was quickly off his line to deny Calvert-Lewin.
After an even first 20 minutes, the Blades took the lead shortly afterwards when CALVERT-LEWIN finished from close range after Heh's cross had cannoned off the post.
The advantage lasted bearly a minute though as GLEAN struck powerfully past Eastwood having been played through on goal.
Calvert-Lewin was proving to be a constant threat to the Cod Army and had three chances in quick succession. Firstly Bleeker saved smartly, then a header went just over the bar, before his last effort from outside the area was inches too high.
In a real end-to-end first-half, Smith rattled the bar at the other end with Eastwood beaten, prior Jake Wright heading against the woodwork for the Blades with the last meaningful action of an eventful opening 45 minutes.
It was the home side who were quickest out of the blocks in the first five minutes of the second period and they were rewarded when MYERS curled home from 25 yards out to put them in front.
Just three minutes later Fleetwood took a firm hold of the game when HANCOX reacted first to score from close range. In their next attack Town could have made it four, but Conway wasted a glorious chance, blazing over.
The Blades got over the shock of conceding twice so quickly, when Cheeseman stung the palms of Bleeker, before a last-ditch block by home skipper Muscat was needed to snuff out Gordon's inviting low centre.
In the 83rd minute Calvert-Lewin almost gave the Blades hope of a late comeback, but he was denied by a reaction save from the impressive Bleeker, meaning it was Fleetwood who advance to the third round.
Blades: Eastwood, Gordon, Kedman, Ishmail (Cockerline 61) Adebowale, Cheeseman, Heh, Calvert-Lewin, Wright (Slew 79), Hinchliffe (Giraud-Hutchinson 89) Ramsey.
Unused: Semple, Ramsdale.