A goal from unlikely hero Jesper Gronkjaer proved to be the match-winner in a game totally dominated by Claudio Ranieri's expensive side.
Joe Cole's 15-yard chip was plucked out of the air by Scott Carson in the third minute before Gronkjaer's deflected effort was acrobatically turned over for a corner by the young keeper, who had an excellent game.
In the 16th minute Eidur Gudjohnsen should have scored. He latched on to a long Glen Johnson ball and forged his way past a static Leeds defence before scooping the ball over Carson, but his effort drifted high and wide of the goal.
Seconds later a Cole special forced Carson to tip the ball over the bar.
Chelsea finally broke the deadlock in the 20th minute with a diving header by Gronkjaer after an excellent run and cross by Johnson.
At the start of the second half a piece of Cole magic on the edge of the penalty area set up Frank Lampard, but the England midfielder somehow managed to put his header over the bar from eight yards out.
Gronkjaer then flashed a right-foot drive inches wide of Carson's left upright in the 52nd minute.
In a rare Leeds attack, substitute Jermaine Pennant went close with a 70th minute free-kick that beat Carlo Cudicini but ricocheted off the post and was cleared.
But The Whites did not deserve a point as they showed no inclination to attack and should have lost by more than the single goal but for Carson.
Leeds boss Kevin Blackwell faced the music after the game and was upbeat about the performance.
"We expected Chelsea to want to put on a show but we looked resolute and handled the pressure when we went behind," he said.
"I felt the longer the game went on like that we might get something from it. But par for the course for us this season, when we had the chance, the ball hits the post and comes out.
"But we had many youngsters out there today and they did a very good job. I just wish we could start the season again.
"I have to say that some of the players getting on the bus now to go home will not be playing for Leeds again. We will need to get in around 14 players for next season.
"It will be easier to get in loan players from the Premiership and we won't be hampered by the transfer window."