Modou Barrow (right) failed to score in five appearances for Leeds last season
Reading goalkeeper Vito Mannone saved an injury-time penalty from Pablo Hernandez to consign Leeds to a first home defeat of the season.
The Spaniard's low effort was easily kept out by the ex-Sunderland keeper after Samu Saiz was felled in the area.
Former Leeds loanee Modou Barrow kept his composure to put the Royals in front in the 85th minute.
Victory for the Royals moved them two points clear of the relegation zone as Leeds slip to sixth.
The late drama was almost totally out of keeping with the opening 75 minutes of the match.
The Royals won it when sub Barrow, who had earlier forced a good save from home keeper Andy Lonergan, finished well after being played in by Joey van den Berg.
Leeds could have taken the lead when defender Pontus Jansson thumped over from a low corner but struggled to create any other clear chances before their penalty.
Jaap Stam's side had slipped into the bottom three on Friday but move up to 20th after just their third win of the season.
Leeds boss Thomas Christiansen told BBC Radio Leeds:
"We knew it would be a difficult game after coming in from two defeats and as you saw in the first half we were too slow with our build-up. We were much better in the second half.
"I believed the team deserved much better than the result we took today. I think we deserved to win.
"It hurts but we have to continue.
"We've got to face the situation and come back stronger. There are a lot of things to improve but I am not concerned."
Reading boss Jaap Stam told BBC Radio Berkshire:
"We're all delighted. If you look at how the team has been doing in the last month it has not been easy but we stayed positive and confident in what we can do.
"The only thing you can say is maybe we should have scored more goals but one was enough to give us the three points.
"We didn't want to give much space away because we know how they like to play and it paid off.
"The win is for the team not for me. They deserve this."
