Neill Collins had given the Blades a lead before a Tom Nichols penalty levelled things up for Exeter City before Che Adams was once again on the score-sheet, sliding the ball past keeper Bobby Olejnik for the winner.
Blades boss Nigel Adkins once again rotated the squad which had won at Cheltenham Town two days previous with most of the starting line-up again playing an hour of football before being subsequently changed. Only George Long in goal played the full 90 minutes whilst Martyn Woolford started at left-back for the injured Bob Harris.
It was the hosts who made the brighter start to the game with United fortunate that both Wheeler and Holmes fired off-target but the more experienced Blades were more successful at the other end. Having won a corner, Woolford delivered into the box with COLLINS thumping header reaching the top corner of the goal.
On the half hour mark the visitors went close to doubling their lead when Baxter, after linking up well with Higdon saw his effort deflect wide and with the first half drawing to a close Freeman looked to score but Oakley headed off the line.
A chance fell for United early in the second half. After Adams was introduced for Higdon, from a Freeman cross, McNulty looked to pounce but left for Basham who missed the target. It was a miss which proved costly, at the other end Wheeler spun away from the Blades defence and was pulled down by Collins in the box. NICHOLS was on hand to send Long the wrong way to equalise.
United continued to pepper the goal, a fortunate ricochet allowed Campbell-Ryce to play in McNulty, but his effort was blocked and in another attack Woolford saw his shot pushed round the post. At the other end Wheeler fired over the top before Adkins rang in the planned changes.
Long was put under pressure from a McGahey back-pass but he managed to keep out Nicholls whilst, at the other end Adams crossed for Calvert-Lewin whom headed over the bar. But on 79th minute the small 192 Blades fans who made the long journey to Devon was left reeling in celebration when a ball over the top saw ADAMS chase one-on-one with the keeper and coolly slot home at his near post; 2-1.
As the game drew to a close Calvert-Lewin almost extended the lead but Egan cleared for the hosts.
Exeter City: Olejnik, Noble, McAllister, Ribeiro, Harley, Oakley, Holmes, Davies, Nichols, Wheeler, Brown. Subs: Butterfield, Nicholls, Reid, Oyeleke, Hamon, McCready, Tillson, Jay, Watkins, Read, Egan, Down, Hoskins.
Sheffield United: Long, Freeman (Dimaio 62), Collins (McGahey 62), McEveley (K Wallace 62), Woolford (McFadzean 62), Campbell-Ryce (Scougall 62), Basham (J Wallace 62), Baxter (Reed 62), Murphy (Calvert-Lewin 62), Higdon (Adams 45), McNulty (Di Girolamo 62).
Attendance: 1,122