United made it three wins from three in pre-season and Che Adams added another to his tally.
The Blades backed up the wins at Ilkeston and Cheltenham Town with a narrow success at Exeter City on Thursday night. Neill Collins gave United the lead before Tom Nichols levelled from the penalty spot but Adams won it by sliding the ball through the legs of home goalkeeper Bobby Olejnik.
The teamsheet showed no surprises from boss Adkins as he rotated the squad again, but there was a late change in goal where Long started. The outfield ten that finished the game at Cheltenham Town kicked off, including Woolford at left-back, covering for the injured Harris.
Exeter made the brighter start, with Long off his line to prevent an early chance, whilst Wheeler and Holmes were both off target with shots from the edge of the box. The Blades, however, were more clinical, opening the scoring with the first corner, won by Murphy. Woolford delivered and COLLINS lost his marker to head into the top corner.
Both sides went close around the half hour, Nichols for Exeter and Baxter's effort being deflected wide after linking up with Higdon, whilst close to the break Oakley headed off the line from Freeman's cross.
Adams replaced Higdon at the break and there was an early chance for the visitors. From Freeman's cross, McNulty stepped over the ball but Basham, arriving late in the box, missed the target.
It was Exeter's turn, though, to score with their first chance of the half. Wheeler got away from the United defence and was pulled down by Collins as he entered the box. Penalty was the decision and NICHOLS sent Long the wrong way to equalise.
A flurry of good opportunities then followed before the planned substitutions. Following a fortunate ricochet, Campbell-Ryce played in McNulty, but his effort was blocked, despite the presence of Collins, Wheeler fired over for Exeter and then a long-ranger from Woolford was pushed around a post by goalkeeper Olejnik.
A McGahey back-pass put Long under pressure but the goalkeeper kept out Nicholls, whilst at the other end an Adams cross saw Calvert-Lewin win a header but the ball bounced over the crossbar.
United, however, regained the lead on 79 minutes with a goal similar to Tuesday evening's opener. A ball over the top of the defence saw ADAMS latch on down the right channel and he coolly beat the goalkeeper at the near post.
A run by Calvert-Lewin almost brought United a third but Egan cleared for Exeter, whilst Di Girolamo did likewise from the right just before the final whistle signalled another Blades win.
Exeter: 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.
Blades: 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 (192 Blades fans)