Luciano Becchio, Max Gradel and Jonny Howson scored the all-important goals in the final 15 minutes to seal United’s first victory in four Championship outings.
On the balance of chances created, Leeds were good value for their win but Rovers deserve tremendous credit for playing a full part in a derby that kept the 27,027 crowd enraptured until the closing stages.
Rovers had seized the initiative at the start of the half and gone ahead within four minutes of the restart courtesy of a fine finish from Franck Moussa after he had been found by a Brian Stock header.
The lead lasted less than a minute, however, with Jonny Howson dragging United level with a drilled shot from 20 yards after the Elland Road captain had charged down a Stock clearance.
Both sides then created chances with Kasper Schmeichel twice coming to United’s rescue with saves from Molussa and Billy Sharp.
At the other end, Max Gradel then twice failed to capitalise on being played through one on one with goalkeeper Gary Woods.
Leeds then regained the lead when Snodgrass picked out Bradley Johnson, who headed down for Becchio to net from close range.
Such is the fragile state of the home defence, however, United knew a fourth goal was required and it duly arrived seven minutes from time when Gradel finished from close range after Billy Paynter’s shot had been blocked by Woods.
Howson then rounded off the win in stoppage time with a fine finish after being played through by Snodgrass.
Leeds manager Simon Grayson said: “He (Gradel) just epitomises what this team is about. He’s got quality but also a great work ethic.
“The way he chases down defenders and works rubs off on his team-mates and he is a breath of fresh air, a joy to work with.
“He’s reaping the rewards for his endeavour and enthusiasm and he’s a great lad to work with.”
Doncaster boss Sean O’Driscoll was left to rue some poor defending from his side and backed Leeds to secure a play-off place.
“But the manner of the goals in the second half disappointed me.
“To concede a goal 30 seconds after you’ve scored and when you look at the DVD we weren’t even ready for the kick-off, in this division you can’t switch off especially against a quality side like Leeds.
“Credit to them, they’ve created chances all afternoon and their front six is probably as good as anything in the league.”
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