Rochdale's half-time substitutions played a major role in this result at Spotland on Saturday.
After United dominated the first half, forcing home goaleeoer Josh Lillis into a number of fine saves, replacements Peter Vincenti and Grant Holt scored the goals that earned Rochdale the points.
With Hammond suspended due to an accumulation of bookings, Belgian Cuvelier made his first start of the season as boss Adkins made just one change following last weekend's victory over Port Vale. Collins and Scougall were deemed fit enough to take places on the bench.
On a bare pitch, United made the better start and dominated the opening 20 minutes, although with nothing to show for the effort. The front two of Sharp and Adams linked up well early on but the latter's shot was blocked. On eight minutes, from Woolford's cross, Cuvelier arrived late in the box and hit the target but Lillis tipped over; from the resulting Woolford corner, the ball took a deflection in a crowded penalty area before striking the back post.
Soon after Reed's 40-yard pass found Adams, who turned inside his marker and struck a controlled half-volley but Lillis again tipped over, whilst Rochdale's first opportunity, on 20 minutes, saw Henderson head wide from Rafferty's cross.
Just after the half-hour the Blades lost Woolford to injury, forcing former Rochdale player Done to slot into an unfamiliar left wing-back role. The remainder of the half became scrappy but with the Blades still in control. The visitors won a number of corners and on 41 minutes, Adams latched on to a mis-placed Rochdale pass and showed great composure before forcing another save out of Lillis.
Rochdale made a double substitution at the break, introducing two attack-minded players, but the Blades continued the first half positivity. On 49 minutes, a low corner from Done saw Basham turn the ball over at the near post and the visitors also win a number of other set-pieces around the penalty area.
Rose shot wide for Rochdale but the Blades were soon back on the attack. Adams fouled as he looked to get on a Sharp pass and the front two combined again soon after but Lillis denied Sharp by diving at his feet.
At the midway point of the half, though, Rochdale grabbed the initiative, thanks to their subs. McNulty began the move on the left and Holt laid off for VINCENTI to curl around Long's left hand, into the bottom corner.
Within a minute, the Blades were back on the attack but from McEveley's break, Lillis saved from Adams once again, whilst for the final 15 minutes Adkins opted for fresh legs in midfield with a double change.
Coutts almost had an immediate impact but the Blades were stung with a second with nine minutes to go. From a right wing corner, HOLT beat Long with a close-range header.
Lund almost added a third after good work from Holt but United could not force any further saves out of Rochdale goalkeeper Lillis, who was named man of the match for his string of saves.
Rochdale: Lillis, Rafferty, McNulty, Eastham, Lund (Bennett 90), Canavan, Mendez-Laing (Holt 45), Allen, Rose, Bunney (Vincenti 45), Henderson.
Unused: Alessandra, Noble-Lazarus, Collis, Camps.
Blades: Long, Brayford, Basham, Flynn (Scougall 75), Sharp, Woolford (Done 32), McEveley, Reed, Adams, Cuvelier (Coutts 75), Edgar.
Unused: Howard, Collins, Campbell-Ryce, Calvert-Lewin.