Irishman Healy's eight-yard downward header from Gary Kelly's cross broke the deadlock in the 74th minute, 13 minutes after Steve Stone had left the bench for his long-awaited debut.
Stone's introduction drew almost as many cheers as Healy's goal and the former England winger hopes to play a part in the play-offs after proving his fitness.
Leeds missed 13-goal Rob Hulse who, along with Jermaine Beckford, was the latest victim of a virus that has affected several players at the club in recent weeks.
On-loan Danny Graham made his first start before returning to Middlesbrough and almost scored in the third minute when his header from the edge of the six-yard box narrowly cleared the bar.
The unlucky striker picked up an Achilles injury early in the game but battled on bravely before being replaced by Ian Moore three minutes before the break.
Leeds dominated possession and stitched together some intricate moves but, not for the first time this season, their finishing left much to be desired. Stephen Crainey and Healy tried the long-range route, Graham was denied by Stephen Foster's vital headed clearance and when Shaun Derry drove the ball across the goalmouth there were no takers.
Derry revelled in the space he was allowed in midfield and was only just too high with a shot from a yard inside the penalty box.
Crewe were fortunate that Madjid Bougherra, their Algerian international central defender, was on top of his game. With Ross Turnbull off his line, Liam Miller tried a chip from distance only for the dependable Bougherra to clear off the line.
Crewe had to wait until the 49th minute of a meaningless game to produce a shot on target but Gareth Taylor's shot was straight at Neil Sullivan.
Bougherra was allowed a free header when he moved forward for a corner, but he too missed the target and Healy made the Railwaymen pay.
Leeds, having used all their three substitutes, finished the game with midfielder Eirik Bakke limping up front.