Rooney's first-half goal and two assists after the break for Andy Dawson's own-goal and Dimitar Berbatov decisive third secured the points for United after Craig Fagan had levelled from the penalty spot.
Chelsea's failure to claim three points at Birmingham on Boxing Day had handed United the opportunity to close the gap on the leaders with victory at the KC Stadium, but Ferguson's team had started the game in third place following Arsenal's 3-0 win against Aston Villa at lunchtime.
Despite making a bright start when Ryan Giggs volleyed Antonio Valencia's cross over the bar on six minutes, United were given a difficult half by the home side.
And Hull should have been awarded a penalty on 21 minutes following a clumsy Wes Brown challenge on Richard Garcia.
Australian forward Garcia had latched onto Craig Fagan's throughball deep inside the United penalty area and Brown's tackle clearly caught man before ball.
Referee Alan Wiley, taking charge of his first United game since Ferguson earned a two-match touchline ban for labelling him 'unfit' in October, waved away the home side's appeals, however, to hand United a reprieve.
Both sides aggressively chased the opening goal, though, and it made for an entertaining encounter.
Seyi Olofinjana had a 25-yard shot saved by United goalkeeper Tomasz Kuszczak before the Pole produced a crucial block to keep out the Nigerian midfielder's close range volley on 28 minutes.
United were just as threatening at the other end. Giggs shot wide from a tight angle before both Darren Fletcher and Rooney had goalbound efforts blocked.
Stephen Hunt then directed a left-foot shot narrowly wide of Kuszczak's far post before United full-back Rafael da Silva, having sprung the Hull offside trap, shot straight at goalkeeper Boaz Myhill from 12 yards.
With the game heading towards half-time, however, Rooney broke the deadlock when he held off Kamil Zayatte's challenge to guide home Fletcher's cross from six yards, two minutes into stoppage time.
The home side were handed a route back into the game on 59 minutes, however, when Wiley awarded Hull a soft penalty.
Rooney's misjudged back pass to Kuszczak, which was cut out by Fagan, prompted the panic in the United back four and his cross to the far post looked set to pick out Jozy Altidore until the American fell to the ground under Rafael's challenge.
Replays suggested no contact had been made, but Fagan stepped up nonetheless to equalise from the penalty spot.
Rooney made up for the error that led to the equaliser, though, by providing the cross from which Dawson scored the own goal that put United on course for victory.
And the England capped an impressive display by teeing up Berbatov for United's third with a clever pass from Wes Brown's clearing header.