The Blades picked up a first point of the season thanks to Billy Sharp's late goal.
The captain struck home a Chris Hussey free-kick with nine minutes to go after Andy Cannon had given Rochdale a first half lead.
For a third consecutive game, Wilder named an unchanged starting line-up. New loanee Chapman, signed from Middlesbrough, was amongst the substitutes. Rochdale's team included former McGahey and Mendez-Laing.
The early battles were even, and so were the chances. Lillis smothered after a neat move involving Fleck, Duffy and Done and O'Connell blocked from McDermott. Long range efforts from Duffy and Cannon also came to nothing.
The first serious chance arrived on 15 minutes and a fortunate ricochet saw the ball drop invitingly for Henderson but Long was quickly off his line to make an impressive save.
Bizarrely, Fleck was booked for a follow through on a Rochdale player when he was fouled - United won the free-kick...work that out! Duffy and Cannon both dragged shots wide as the match remained in the balance.
As half-time approached, though, Rochdale claimed an advantage. Henderson's shot from the edge of the box, possibly deflected, spun away from Long's grasp and CANNON reacted first to round the goalkeeper and slot home at the Kop end.
Early in the second half the sides exchanged chances from crosses but McGahey for the visitors and Done for the Blades were off target.
Just before the hour Chapman was introduced for his debut and the Blades were now on top, trying to force a leveller. On 65 minutes, from Duffy's deep cross, Clarke, at full stretch, headed just wide and then a cross from Sharp was too high for the striker.
Rochdale, expectedly, were happy to slow down the action at every opportunity but they were stung on 81 minutes, following Canavan's foul. Hussey swung in a free-kick from the right and as the visitors appealed for offside, SHARP slotted into the top corner.
Appeals for a penalty in front of the Kop, as Clarke and McGahey clashed, were waved away and Rochdale had a chance when Andrew headed wide a McNulty cross.
Late on, Basham tried to thread a ball through to Sharp but Lillis was quickly off his line and three minutes of added time failed to herald another chance.
Blades: Long, Brayford, Hussey, Fleck, O'Connell, Basham, Sharp, Done (Chapman 59), Wilson, Duffy (Scougall 68), Clarke.
Subs: McNulty, Ramsdale, Wright, Coutts, Freeman.
Rochdale: Lillis, Rafferty, McNulty, Canavan, McGahey, Andrew, Mendez-Laing (Odelusi 68), McDermott, Allen, Cannon (Camps 78), Henderson.
Subs: Tanser, Thompson, Logan, Morley, Bunney.