United made it six games unbeaten on the road - thanks to a solid defensive display and two goals from midfielder Conor Coady.
The loanee converted two Jamie Murphy crosses to ensure the Blades returned to winning ways.
Ironically, it was two goals from Tony McMahon that earned the Blades a 2-0 victory at Crawley in the corresponding fixture last year.
Chief Clough made three changes for the trek to Sussex. McGinn, Davies and Porter were all recalled - Scougall, Flynn and Baxter dropped to the bench. Crawley's starting XI included former Blades loanee Clarke and ex United junior Kyle McFadzean - the duo combined to register the first chance on three minutes, the latter meeting the former's free-kick but Howard pushed away.
On six minutes Clarke cut in from the right and his shot hit Collins but Crawley's appeals for a penalty were ignored, whilst the home side's early spell of pressure came to nothing.
United's first attacking threat was a run out of defence by Maguire but he fired wide under pressure and then the deadlock was broken on 19 minutes. Murphy's trickery earned him space on the left and his cross was only cleared as far as COADY, whose subsequent body position and shot beat the home goalkeeper from 15 yards.
With five across midfield, the Blades then set about controlling the game and keeping Crawley out, although the home side created a couple of chances. Clarke fired over and a 25-yard free-kick from Drury was low and found the sidenetting.
As half-time approached, United's control continued and the home side were limited to just one more effort, Connolly firing over after a corner was only half-cleared.
Early in the second half Collins headed a Davies corner wide and Freeman picked up the game's first booking for a foul on Torres before Crawley looked to get back into a rhythm. On 55 minutes, a shot from Bulman was deflected nicely for Drury, whose blast was saved by the feet of Howard and Tubbs was unable to convert the loose ball.
The home side's progress was stunted somewhat, though, with a second Blades goal on 63 minutes. Again, Murphy was the architect, he took the attentions of three defenders before delivering a deep cross to the back post where COADY was arriving in the box to volley home, with the aid of a deflection.
With 15 minutes remaining McFadzean went close with a shot on the turn, despite being under pressure from Maguire and Porter he got a shot away which was pushed away by Howard. United, however, were still on top and went close to a third from Davies before the first Blades change arrived in the final ten minutes, Paynter taking over from Porter.
The Blades bench thought there should have been a penalty when Connolly brought down Freeman but the referee was unconvinced and moment later goalkeeper Jones was forced to save from Murphy.
The closing moments - plus four added injury-time minutes - saw little in terms of Crawley attacking but there were a late debuts for 18-year-olds Dimaio and Khan and a booking for Maguire. The final whistle followed seconds later to make the long journey north a happy one.
Crawley: P. Jones, Sadler, M. Connolly, McFadzean, Clarke, Torres (Proctor 66), Drury, Walsh, Bulman, Tubbs (Fallon 79), M. Jones.
Unused: Fallon, Boateng, Maddison, Dicker, P. Connolly.
Blades: Howard, Brayford, Maguire, Doyle, Porter (Paynter 81), McGinn, Collins, Coady, Davies (Dimaio 90), Murphy (Khan 90), Freeman.
Unused: Flynn, Baxter, Scougall, Long.