It was a rare touch of class from the home side, who had worked hard but without much inspiration.
Peter Gilbert's own goal a minute into the second half, set them on the way to their second win over Christmas and stretched their unbeaten run to four matches despite conceding a last-minute goal to sub Stevie Crawford.
Plymouth could feel aggrieved that they had to make the long trek back to the West Country with nothing to show. They had played the better football but paid the price for failing to turn pressure into real chances - they only had two efforts on target before Crawford's consolation.
That was partly down to solid defending from Paul Butler and Matthew Kilgallon and partly because their often slick build-up wasn't reflected in their finishing.
Leeds will be happy with the win and with the shadow of dropping into the relegation zone now lifting, they might be able to push on.
Expectations were high among the Elland Road faithful after their stirring 3-2 Boxing Day win at Sunderland.
But it didn't take long for hope to fade after the game began. A thoroughly dour first half had people speculating how much more entertaining it would have been to be at home watching Babe or even queuing to pick up a bargain in the sales.
With recent signing from Coventry, Bjarni Gudjonsson, looking as though he at least understood what football is supposed to be, Plymouth produced the little constructive play on show and it was fitting that it was they who created the first moments of excitement even if it did take 28 minutes.
Marino Keith reacted quickly in an unpromising situation and managed to get a flick on goal that surprised Neil Sullivan, but the Leeds keeper managed to clutch it to his chest.
Lee Hodges also went close with a near-post flick while the only promising moves for Leeds came from teenager Aaron Lennon who went on a couple of sparkling runs but they failed to produce anything like a scoring chance.
Other than that Leeds were content to hit hopeful balls towards Brian Deane, who looked to be suffering after a collision with Romain Larrieu and seldom got the better of Paul Wotton.
The second half started spectacularly with Healy getting to the by-line and pulling the ball across the goal. It seemed to be going safe when Gilbert tried to turn it for a corner but only managed to direct it into his own net.
That sparked a livelier match with Jermaine Wright hitting the post, Frazer Richardson and Danny Pugh making good runs and Plymouth piling on the pressure.