Whites boss Kevin Blackwell made one change to the side that defeated Plymouth, with Nathan Blake making his debut as a replacement for Brian Deane, who is likely to be out for six weeks with a shoulder injury.
Poor finishing and strong defence meant the ball just wouldn't go in the net for United and Leeds' misery was complete when skipper Paul Butler was sent off for a second yellow card six minutes from time.
The difference between the sides was in the quality of the finishing, with Dean Ashton and Mark Rivers taking their combined total for the season to 27, only four fewer than Leeds' total for the campaign.
After the dour midweek fare against Plymouth, Leeds matched Crewe's passing game and served up some entertaining football, making full use of the rain-slicked surface to keep the ball moving.
Crewe always looked more controlled and accurate in their work, but Leeds were high tempo and with Lennon and David Healy always dangerous from the flanks, and new loan signing Blake holding the ball up well, they produced plenty of chances in the first half.
But they lacked a clinical finisher like Ashton. Crewe's leading scorer missed an early chance but made no mistake when he put his side in front in the 17th minute.
He earned the goal from old-fashioned persistence, harrying Matthew Kilgallon as the Leeds defender tried to usher the ball out for a goal-kick.
Ashton managed to deflect it off Kilgallon for a corner and when Kenny Lunt swung in the kick, he met it first time and the ball flew past Neil Sullivan, taking the Crewe striker to 19 for the season.
Leeds didn't let their heads drop and attacked the visitors' goal almost non-stop with Lennon and Healy bringing good saves out of Clayton Ince, while Richard Walker produced a last-ditch tackle to deny Sean Gregan.
Lennon had the better of Chris McCready and put three superb balls across the Crewe box in the first ten minutes after the break, but no-one was able to get a touch and instead of drawing level, they found themselves falling behind to more slick finishing.
Lunt drilled a free-kick into the penalty area, Leeds blocked it but didn't clear and Rivers popped up to stab it home.
Kevin Blackwell sent on Iceland international Gylfi Einarsson for his debut, teenager Simon Walton and striker Michael Ricketts, but despite plenty of pressure they were unable to find the net.