United's second victory in four days saw them climb back into the top six where many pundits expect them to be come the end of the season.
Doncaster Rovers could be fighting a different sort of battle next May – one of survival – unless they can start converting chances into goals.
Rovers haven't scored in their last three games at the Keepmoat Stadium and have now lost five league games in succession.
They dropped into the bottom three last night for the first time.
Rovers' boss Sean O'Driscoll rung the changes following the club's 2-0 home defeat against Southampton at the weekend.
Centre-back Adam Lockwood and midfielders Mark Wilson and Martin Woods all started for the first time this season.
United started with the side which beat Watford at Bramall Lane to claim their first win in five league games.
Rovers made the early running, knocking the ball about well. But the first chance of the game fell to United's £4.5m striker James Beattie on eight minutes – Rovers keeper Neil Sullivan making a comfortable save from his low angled shot.
Rovers midfielder Richie Wellens picked out striker Darren Byfield in the area, but he shot high and wide under pressure.
United took the lead on 14 minutes when Rovers left-back Gareth Roberts put into his own net when trying to cut out Danny Webber's left-wing cross into the box.
Greg Halford latched on to a half clearance three minutes later but shot tamely at Sullivan from 25 yards.
Rovers went close to an equaliser on 19 minutes. Centre-back Matt Mills climbed above the United defence to get a powerful header on goal from a corner by skipper Brian Stock. Keeper Paddy Kenny did well to palm the ball to the far post where Byfield somehow shot wide from a yard out.
There was another let-off for United when Stock worked his way towards goal before unleashing a long-range effort which beat Kenny but hit the underside of the bar. The loose ball fell kindly for Price but he fluffed the chance.
Rovers again went close to the equaliser on 29 minutes.
Woods picked out Price in the box with a delightful chip. The striker's first touch let him down but he still managed to test Kenny – the ball striking him on the leg as he tried to smother the low angled shot.
United had got little change out of the Doncaster back-four before Webber carved out a chance for Beattie - who headed wide - at the far post just before the break with a cross from the left.
United doubled their lead on 59 minutes when Stephen Quinn latched on to Beattie's through ball in the box and ran on before beating Sullivan with a clinical finish.
Said Quinn: "We came here full of confidence following the win over Watford.
"It was a bit like chasing shadows in the first half because we worked so hard against Watford and the game was still in my legs.
"But the second half we started turning on the style and started passing the ball and we eventually broke them down for the second.
"It felt great to score. It was a great ball in from Beatts and it sat up nicely for me and I just slotted it in. It was a great feeling scoring in front of all the fans as well."
Rovers' Mark Wilson, who was entitled to feel pleased with his contribution, tested Kenny as Rovers pushed forward again in search of a reply.
Man-of-the-march Woods and Wellens, who again ran himself into the ground in the Rovers cause, both shot wide and Byfield shot over from in front of goal in stoppage time.
Saturday's match at Oakwell will take on added significance for Rovers following this defeat.
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