Phil Brown's side, whose run of eight wins from 11 games has taken them to within reach of the Premier League, carved open United on seven minutes. Skipper Ian Ashbee threaded the ball through to on-loan Manchester United striker Fraizer Campell, but the youngster's first touch was poor and his tame shot from just inside the area was safely scooped up by Paddy Kenny.
Caleb Folan stuck out a foot to deflect a Michael Tonge free-kick away from Beattie, before the ex-Everton striker almost found a way through with a close-range shot.
Tonge was allowed too much space as he cut inside from the right flank, but his shot on the run had pace but flew high over the target from 20 yards.
Hull should have snatched the lead on 29 minutes. Full-back Sam Ricketts shrugged off two challenges and his cross from the right was cleared to the lurking Dean Marney, who sliced his shot wide of the target from 16 yards.
United squandered a chance in the 39th minute as David Cotterill was given space on the right and his precise cross found the unmarked Billy Sharp, who headed over from six yards.
The Sheffield side were down to ten men two minutes into time added on after Morgan hauled back Campbell a yard outside of the area. The centre back, who had been booked for a foul on the striker in the 25th minute, was shown a second yellow by referee Phil Dowd after a discussion with his assistant.
Boaz Myhill pulled off an eye-catching one-handed stop to keep out a Sharp header before United swept ahead in the 50th minute in spectacular fashion. John Halls' cross was headed powerfully into the box by Beattie and little midfielder Quinn raced onto the loose ball to powerfully volley past Myhill from 16 yards.
United went 2-0 up 20 minutes later after the lively Sharp was brought down in the area by David Livermore, and Beattie slammed in his 22nd of the season from the penalty spot.