Keane headed a Gary Neville cross from the right into the far corner of the net in the 81st minute, giving Leeds goalkeeper Paul Robinson little chance.
Man Utd had struggled to get past a determined Leeds defence. They also missed chances when striker Diego Forlan's shot went over the bar and Salomon Olembe cleared a late Ruud van Nistelrooy kick off the line.
Paul Scholes also shot against the Leeds bar from inside the six-yard box in stoppage time.
The opening forty-five minutes were a relatively tame affair, with Sir Alex Ferguson's side in control in terms of possession, but lacking the invention to break down a determined Leeds.
After Leeds' early season problems, on and off the pitch, this was a performance full of character, with midfielder David Batty, winger Jermaine Pennant and left back Salomon Olembe outstanding.
However, strikers Mark Viduka and Alan Smith were subdued by Rio Ferdinand and Mikael Silvestre, Ferdinand showing no after-effects from the controversy surrounding his drug test no-show.
The champions were without Ryan Giggs with a virus, which led to Cristiano Ronaldo back in the starting line-up, with the Portuguese star just as much a figure of hate for the Whites fans as Rio Ferdinand. Nicky Butt dropped to the bench.
Ronaldo had a fifth minute penalty claim rejected by Graham Poll. Ronaldo gave Zoumana Camara the slip before falling to Gary Kelly's challenge, Poll giving Kelly the benefit of the doubt.
When Ronaldo fell in the penalty area for the second time in nine minutes while under another challenge from Gary Kelly, referee Graham Poll had had enough and booked the winger.
Leeds had James Milner making only his second start and his first of the season, with Jody Morris serving a club suspension.
Leeds had to wait until the 38th minute for their first shot, Dominic Matteo's low drive being deflected for a corner.
The Reds lost Quinton Fortune with a knee injury received in a high tackle which earned Pennant a booking and John O'Shea came on for him in the 39th minute.
Batty was also shown the yellow card in a disjointed first half littered with stoppages.
Robinson, in the Leeds goal, had to wait until the 50th minute to make a save, Scholes shooting powerfully but straight at him.
Ronaldo clipped the angle of post and bar from the edge of the penalty box and there were bookings for Smith and Seth Johnson as Leeds' frustration spilled over.