Darius Henderson scored twice as Sheffield United came from 2-0 behind to keep alive their slim hopes of staying in the Championship.
Noel Hunt poked into the top corner from close range to give promotion-chasing Reading the lead before Hal Robson-Kanu stroked in a second.
United hit back through Henderson's strike and Lee Williamson's tap-in.
Henderson met Matt Lowton's cross to put the visitors in front and hold off relegation for five more days.
Third-bottom United trail Crystal Palace and Doncaster by six points in the Championship with two games to play, but the Blades have an inferior goal difference of -31, compared to Palace's -22 and Rovers' -23.
Though the defeat prevented Brian McDermott's Reading from cementing a play-off place, another point from their final two fixtures will be enough to extend their season.
It looked like Reading would coast to victory as they dominated early on, Shane Long threatening when he pounced on a poor piece of control from Stephen Quinn 25 yards from goal, but he fired over.
Hunt opened the scoring in the ninth minute after Long played in his strike partner on the left and the Republic of Ireland international cut inside before flashing a shot high between goalkeeper Steve Simonsen and his near post.
The pressure was relentless from the Royals and it was no surprise when Robson-Kanu doubled the lead in the 20th minute.
Long was fouled but the referee played the advantage, allowing Jobi McAnuff to put in a low cross which Steve Simonsen could only divert into the path of Robson-Kanu, who hooked the ball into the empty net.
The Blades looked ragged and had barely made it into the Reading half when they pulled one back with their first shot, on the half-hour mark. Former Reading striker Henderson bundled through the Berkshire side's defence and chipped a shot wide of Alex McCarthy and into the corner.
Suddenly United found reserves of fight that had previously been non-existent.
And they deservedly drew level at the start of first-half stoppage time when Quinn made progress down the left before finding Williamson breaking into the area, from where the midfielder sent a left-footed shot into the net.
And Henderson, who had not scored in six previous appearances this season, completed the comeback when he tapped in on the line early in the second half.
The Reading players were barely able to hide their shock and began to bicker amongst themselves as Sheffield United launched a rearguard action, making last-ditch challenges and throwing bodies in front of shots.
Blades youngster Jordan Slew thought he had made it four for United but his slotted shot into the empty net after the Reading keeper's clearance had come off Henderson was chalked off for a foul in the build-up.
Henderson was then denied a hat-trick by a brilliant save from McCarthy before Reading substitute Brian Howard almost relegated his former side when he struck the crossbar with a floated effort.