Captain courageous Roy Keane headed Manchester United's winner with nine minutes to spare, after Peter Reid's Leeds had given their all.
Keane arrived at the far post to meet Gary Neville's high cross from the right and head into the opposite corner.
It settled a disjointed match in which chances were few, though Paul Scholes shot against the Leeds bar from inside the six-yard box in stoppage time.
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, who was suffering from a virus. Nicky Butt dropped to the bench and in came Phil Neville and Cristiano Ronaldo.
Leeds had James Milner making only his second start and his first of the season, with Jody Morris serving a club suspension.
Ferdinand was given a hostile reception by Leeds fans on his return to Elland Road.
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.
The next time Ronaldo and Kelly clashed inside the box Ronaldo dived and was shown the yellow card.
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 left the bench 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.