Goals from Noel Hunt and Hal Robson-Kanu put Reading into an early lead but the Blades rallied to level at the break thanks to goals from Darius Henderson and Lee Williamson.
Henderson then added a third early into the second half to give Micky Adams' side a fantastic result which keeps their slim hopes of survival alive.
United are six points from safety with an inferior goal difference but can hope to catch Doncaster if the Yorkshire side suffer some heavy defeats in their final two games.
The defeat prevented Brian McDermott's men from cementing a play-off place but another point from their final two fixtures will book their place in the lottery.
Shane Long had the first effort on goal when he pounced on a poor piece of control from Stephen Quinn 25 yards from goal but fired over the top.
And it was strike partner Hunt who opened the scoring in the ninth minute.
Jobi McAnuff fed Long who in turn played the ball out to Hunt on the right-hand side.
The Republic of Ireland international cut inside his man before flashing a shot high between Blades goalkeeper Steve Simonsen and his near post.
Simonsen was then at his best to bat out a fierce Jem Karacan drive and get to his feet quickly to tip Hunt's follow-up around the 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 a good advantage to allow McAnuff to stride on and put in a low cross. Simonsen got his hand to the ball but could only divert it into Robson-Kanu's path and the youngster hooked it into the empty net.
The Blades had barely made it into the Reading half but pulled one back with their first shot on the half-hour mark.
Former Reading striker Henderson made the goal all on his own, bulldozing into the area from the left before rolling a scuffed shot wide of Alex McCarthy in the Reading net.
Henderson then saw another effort well saved by McCarthy as the visitors belatedly showed some urgency.
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 and the midfielder sent a left-footed shot into the net.
Adams must have been heartened by his side's fightback and they took the lead for the first time six minutes into the second period.
Williamson swung in a fabulous free-kick from wide on the left which McCarthy clawed away from the corner but Bjorn Helge Riise was on hand to pick out Henderson for a tap-in on the line.
McAnuff led a break clear for the shell-shocked Royals but could not pick out Long before Blades youngster Jordan Slew had the ball in the net but saw it 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 killed off his former side when he struck the crossbar with a floated effort.