Jon Dadi Bodvarsson gave Reading an early lead but centre back Pontus Jansson levelled for Leeds shortly before half time.
In an entertaining contest, Leeds went ahead 11 minutes after the break through a firm Pablo Hernandez strike.
But Reading equalised two minutes later when Leeds midfielder Eunan O’Kane diverted a Leandro Bacuna shot into his own net.
Leeds had won just one of their past 12 league games and only one in six since Paul Heckingbottom replaced Thomas Christiansen as head coach last month.
Reading had won only once in 15 league outings and not won at home in the Championship in eight attempts, a run that stretched back to late November.
Leeds made much of the early running, with Ezgjan Alioski prominent on the left flank.
Alioski cut into the home area before firing narrowly wide then forced a fine save from goalkeeper Anssi Jaakkola at his near post.
Reading replied, also using the wings, but good work by Bodvarsson on the right ended with a poor cross.
But the hosts at last got it right when they went ahead in the 16th minute.
Sone Aluko played a penetrative pass through the Leeds defence for Bodvarsson to run on to.
The Iceland striker took his time before planting a low shot past keeper Bailey Peacock-Farrell for his 10th goal of the season.
Reading almost extended their lead soon after, with Peacock-Farrell saving smartly from Bodvarsson and then George Evans seeing his follow-up effort blocked.
Barrow should also have done better, after seizing on an error by Laurens De Bock, but his early shot was beaten away by Peacock-Farrell.
The 21-year-old keeper also saved superbly from Evans’ powerful 25-yard shot.
Leeds weathered the storm and were rewarded with an equaliser in the 43rd minute.
Adam Forshaw set up Jansson, who clipped the ball home from close range despite the valiant attempt by Chris Gunter to head it off the line.
Leeds emerged the more positive after the break and went in front in the 56th minute.
Samuel Saiz ran across the home area before releasing Hernandez, who beat Jaakkola with a rising cross-shot.
However, their advantage lasted only two minutes.
Bacuna’s low drive appeared to be flashing wide of the goal until O’Kane stuck out a leg to direct it into his own net.
Leeds could have clinched a much-needed victory in the closing stages but Jaakkola made a sprawling save to thwart Alioski.
Substitute Pierre-Michel Lasogga then charged down a Jaakkola clearance but the ball luckily rebounded off a post and back into Jaakkola’s grasp.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.