In the day's other early kick-off in the Championship, Huddersfield shared a 0-0 draw with Sheffield Wednesday.
Steve Bruce's Hull side are in the thick of the promotion race and cemented themselves in second place heading into 2013 with this win, eventually brought about by goals from Corry Evans and David Meyler.
Prior to Evans' 52nd-minute opener it had looked as though the one thing to have blighted Hull this season - a dismal lack of goals - would haunt them again, but once the seal was broken they did not look back.
They were ably assisted by Neil Warnock's Leeds, though, who over Christmas have gone from promotion candidates to mid-table fodder, with this one of their most anaemic performances of the season.
United had one notable effort - a Tom Lees half-chance - and with 17-goal Luciano Becchio benched, spent the game chasing shadows and were lucky to end the game with 11 men.
In Saturday's other npower Championship early kick-off, Sheffield Wednesday extended their unbeaten run to four matches but were given a helping hand by referee Mick Russell in another fiercely-contested Yorkshire derby.
Wednesday, who have climbed out of the relegation zone after three straight wins over the Christmas period, should have been reduced to 10 men midway through the first half when key player Jeremy Helan was shown a second yellow card.
But Russell did not realise he had already booked the on-loan Manchester City midfielder and amid furious protestations from Huddersfield players and management, the Herefordshire official allowed Helan to play on.
Huddersfield, now without a win in nine league matches, almost snatched all three points in the final minute when substitute James Vaughan flashed a volley inches wide.
But Wednesday substitute Mamady Sidibe forced Huddersfield goalkeeper Alex Smithies into a superb save with a header moments earlier and a draw was a fair reflection of an entertaining encounter.