Jamal Campbell-Ryce's first Blades goal earned three more Sky Bet League One points for Nigel Clough's side.
There was an element of fortune as Campbell-Ryce's goal, six minutes from time, took a telling deflection off Stephen Dawson.
However, the goal ensured the Blades are now unbeaten in five, including four in the league.
United's starting XI showed one change from the previous fixture - the pre-international week trip to Preston - with Alcock replacing Higdon, who dropped to the bench. The change in personnel prompted a reshuffle with Baxter and Murphy the most advanced pairing and Davies and Campbell-Ryce in wide areas.
The new front two were prominent early on. Murphy thought he should have had a penalty inside the opening two minutes and Baxter headed over an inswinging free-kick from Davies. Rochdale's first opportunity was the result of breakdown in communication and McEveley not dealing with a Vincenti cross, but Henderson could not take advantage.
A spell of Rochdale pressure saw Bennett's shot deflected wide and Henderson meet the resulting corner but the Blades were soon on top, Baxter just failing to get on the end of a Basham flick.
Davies whipped in a number of deliveries and Campbell-Ryce was causing issues from both flanks. Murphy curled wide on 35 minutes, quickly followed by a long-range effort from Baxter, which was also wide, but goalkeeper Logan was at full stretch.
As half-time approached, further deliveries from wide areas tested the visitors. The ball deflected off Vincenti to Logan, Eastham cleared over his own crossbar and a header from Collins was wide.
The Blades began the second half on the offensive and forced Rochdale onto the back foot. An effort from Campbell-Ryce was wide whilst the same player delivered a cross for Basham but Logan was ideally placed.
McNulty and Flynn were introduced within the space of a couple of minutes and on 66 minutes a Baxter corner was well met by Collins but Logan again saved.
On 71 minutes, Rochdale went tremendously close. A long kick from Logan was flicked on by Vincenti and Henderson rattled the crossbar with a 25-yard half-volley. Another spell of pressure from the visitors failed to break the deadlock and United were quickly back on the attack.
Wallace took over from Basham and a free-kick from the edge of the box saw Baxter's shot collected by Logan, but the goalkeeper could do little with United's opening goal on 84 minutes. McNulty and Alcock had linked up on the right but the ball squirted out to the left where CAMPBELL-RYCE's curler deflected off Dawson, spun beyond the goalkeeper's reach, before dropping into the corner of the net. The United goalscorer was subsequently booked for whipping off his shirt in celebration.
Rochdale made a double change but United were again an attacking force. Flynn's shot flew wide and a shot from Wallace was blocked.
Three minutes of added time was announced but Rochdale could manage just one effort when Vincenti met Done's cross but Howard made a flying save to protect another three point haul.
Blades: Howard, Alcock, Basham (Wallace 74), Doyle, Murphy (Flynn 65), Baxter, Collins, Davies (McNulty 63), McGahey, McEveley, Campbell-Ryce.
Unused: Harris, Higdon, Reed, Turner.
Rochdale: Logan, Rafferty (Kennedy 43), Bennett (Fenelon 86), Eastham, Vincenti, Dawson, Done, Tanser, Allen (Andrew 86), O'Connell, Henderson.
Unused: Lancashire, Andrew, Hery, Musangu, Fenelon, Bunney.