The Irishman curled a magnificent free-kick past former United keeper Neil Sullivan after 20 minutes to gain sweet revenge for Rovers' 1-0 win at Elland Road in January.
It was the first meeting between the clubs in Doncaster since 1955 and produced a pulsating match, with Leeds often having to defend desperately.
Rovers had two penalty claims turned down, hit the post, had a header cleared off the line and saw Casper Ankergren pull off a string of special saves.
But Leeds showed the kind of grit they need if they are to work their way into a play-offs position and, having taken 14 points from their last seven matches, moved to within a point of 6th-placed Tranmere with a game in hand.
Gary McAllister was forced to make three changes from the side that drew with Brighton, Jonathon Douglas moving into the holding midfield role for David Prutton, Frazer Richardson taking over at right back from Darren Kenton and Paul Huntington replacing Rui Marques in the centre of defence.
Rovers made a lively start with some precise passing and Paul Heffernan had two early chances, the first stabbed just past the post and the second superbly saved by Ankergren.
But Leeds were also producing better football than on Saturday and when Douglas won a free-kick on the edge of the area, Sheehan stepped up to the mark and duly scored.
Rovers almost equalised straight from the restart but again Ankergren pulled off a superb one-on-one save to deny James Coppinger.
It was a thoroughly entertaining game and the longer it went, the more comfortable Leeds looked. They should have extended their lead but Jonny Howson fired straight at Sullivan after being set up by Richardson.
Rovers started the second half like a rocket and within two minutes Richard Wellens shot inches wide and Huntington deflected a free-kick on to his own post and away for a corner.
Soon after that, Steve Roberts squandered the easiest chance of the lot when he completely missed the ball with the goal at his mercy.
Ankergren pulled off another brilliant save to deny Jason Price and substitute James Hayter put the rebound over the bar.
Leeds were under intense pressure but they worked hard and the defence held firm to pick up three invaluable points.