Vito Mannone saved a stoppage-time penalty to ensure Mo Barrow's goal was enough to end Reading's winless run and inflict a third straight Sky Bet Championship defeat on former club Leeds.
United were handed a lifeline after Samuel Saiz was brought down in the box but Mannone kept out Pablo Hernandez's weak spot-kick to give the Royals their first win in seven games.
Barrow failed to make an impact during a five-game loan spell with Leeds towards the end of last season but he showed United what he was capable of in a match-winning cameo off the bench.
Andy Lonergan, making the first start of his second spell at the club, had kept Leeds in the match only for Barrow to deny him a clean sheet and increase United's woes after a strong start to the campaign.
Last season's play-off finalists Reading started the game in the relegation zone but their performance at Elland Road suggested they were occupying a false position.
The Royals created the only clear-cut chances of the first half, only to be denied twice by Lonergan.
After Roy Beerens had curled a shot over in a promising position, Jon Dadi Bodvarsson made light work of an attempted Liam Cooper challenge before shooting straight at Lonergan.
A minute later the Leeds goalkeeper was at full stretch to keep out Sone Aluko's low strike after Reading had once again caught the United defence short.
The hosts rarely threatened in the opening 45 minutes, with only lone striker Pierre-Michel Lasogga getting sight of the Reading goal.
The German had a weak header comfortably saved by Mannone early on and then curled a long-range shot wide as Leeds struggled to break the visitors down.
The pace of the game lifted after the restart with Leeds midfielder Eunan O'Kane curling wide and Dave Edwards immediately firing over an even better opportunity at the other end.
Bodvarsson and Leandro Bacuna failed to test Lonergan with efforts but former United loanee Barrow went closer when he fired across goal within a minute of his introduction.
Longeran brilliantly tipped over another Barrow shot, while Leeds substitute Jay-Roy Grot was denied a tap-in by a brilliant sliding challenge by Bacuna as the game became stretched.
Pontus Jansson failed to keep a close-range shot down and Saiz saw a diving header saved by Mannone during Leeds' best spell of the game.
There was a sense a goal was coming and it was Reading who grabbed it six minutes from time with Leeds incensed.
The hosts were still protesting for a free-kick for a foul on Hernandez when Joey van den Berg slipped in Barrow and the forward slid a shot under Lonergan.
Leeds responded positively and looked set for a point after a mazy Saiz run was halted by a foul, only for Mannone to guess the right way to keep out Hernandez.