Goals from Noel Hunt - who flashed a shot between Blades goalkeeper Steve Simonsen and his near post - and Hal Robson-Kanu, who hooked it into an empty net, put Reading into an early lead but the Blades rallied to level at the break thanks to goals from Darius Henderson and Lee Williamson.
Former Reading striker Henderson made the first 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. Williamson then sent a left-footed shot into the net after good work from Stephen Quinn.
Henderson added a third early into the second half - a tap-in on the line - 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.
Source: PA
Source: PA