Che Adams scored the decisive goal, as the Blades completed a first league double of the season at the Keepmoat Stadium on Saturday.
Adams starting up front in place of the injured Billy Sharp poked home just before the break as the Blades gained a deserved success in having dominated much of the South Yorkshire derby.
For the short trip down the M18, boss Nigel Adkins made four changes to his starting XI. Dominic Calvert-Lewin made his full United debut, whilst Louis Reed, Jamal Campbell-Ryce and Che Adams were all recalled at the Keepmoat Stadium. Chris Basham, Paul Coutts and Conor Sammon dropped to the bench, whilst former Rover Billy Sharp missed out with a foot injury.
On a bitterly cold afternoon, it was the Blades who had the first shot on goal. Reed's cross was controlled by Baxter who then tried to beat Neal with a lob, but the goalkeeper tipped it over for a corner. The Blades continued to force the opening exchanges and came even closer to opening the scoring when Collins headed against the crossbar from Baxter's inswinging corner.
But with a swirling wind going round the Keepmoat, United were almost caught out by a long ball forward by Taylor-Sinclair, but having got in behind Edgar, Williams was eventually crowded out and the danger averted. At the other end, Calvert-Lewin headed into the side netting at the back post from Brayford's deep cross.
Despite enjoying the lion share of possession and appearing to be gaining the upper hand, the Blades had two scares in quick succession midway through the first-half, first Tyson got the better of Edgar before Williams saw his goal bound shot blocked, then Williams beat Long to Evina's cross only for Edgar to hack clear off the line.
As the half progressed, the home faithful continued to grow more frustrated as United controlled the game and that dominance was rewarded in the 42nd minute with a well taken goal. Baxter got hold of the ball in midfield and spotted the run of ADAMS, who got the better of the retreating Butler before toe poking past the advancing Neal.
Doncaster made a change at the break with Alcock replacing Butler, a switch that saw Stewart playing in a more advanced role. The first meaningful action of the second period saw Collins head at goal from Hammond's cross. For Rovers, Gooch switched play to Stewart who stung the palms of Long at his near post.
The home side had started the second-half brightly and had their best chance of the game in the 57th minute. Stewart and Gooch combined on the right, before the latter whipped in an inviting ball that just eluded the outstretched foot of Middleton. On the hour, Alcock went into the book for a cynical lunge on Reed.
Hammond became the first Blade to go into the book for a foul on Mandeville, as the game became scrappy. With 18 minutes remaining United had a golden opportunity to double the advantage, Adams threw a dummy which saw him get the better of his marker and he teed up Reed who was denied by Neal's outstretched leg.
The hosts continued to be frustrated as a flurry of substitutes took place as the game entered its latter stages. In the 88th minute, United suffered a scare, as both Tyson and Mandeville failed to capitalise after Edgar failed to deal with Alcock's low cross from the right, whilst Baxter high and wide as four minutes of injury-time we signalled by the fourth official.
With the 3,784 Blades fans in full voice, the added time passed without incident as United professionally saw the game out and deservedly returned to winning ways.
Donny: Neal, Evina, McCullough, Taylor-Sinclair, Butler (Alcock 45), Middleton, Williams, Tyson, Gooch (Mandeville 62), Stewart (Chaplow 76).
Unused: Lund, Lecygne, Stuckmann, Davies.
Blades: Long, Brayford, Baxter, Collins, McEveley, Campbell-Ryce (Flynn 74), Reed (Basham 82), Calvert-Lewin (Woolford 85), Adams, Edgar, Hammond.
Unused: Howard, Coutts, Done, Sammon.