James Chester and David Meyler put the hosts ahead inside 13 minutes, but Chris Smalling and Wayne Rooney put David Moyes' side back on level terms in a frenetic opening 26 minutes.
Former United trainee Chester put through his own net 21 minutes into the second period to put the Old Trafford club into sixth position in the Premier League.
Central defender Chester only made one appearance for the Red Devils, as a League Cup sub against Derby in 2009, and gave the Tigers a fourth-minute lead.
Alex Bruce headed a corner back across goal, and Chester volleyed home from close range for his first Premier League goal.
The second was calamitous from United's perspective. Jonny Evans, who scored an own goal on Boxing Day last year, failed to clear his lines and then managed to poke Meyler's scuffed shot past David de Gea.
Rafael then went off with a pulled groin, with Antonio Valencia dropping to right-back and Adnan Januzaj coming on. This enforced tactical alteration helped United, who were soon level.
Smalling climbed high above Curtis Davies to head Rooney's free-kick into the net on 19 minutes.
Danny Welbeck and Wayne Rooney then combined on the edge of the penalty area before the latter unleashed an unstoppable right-foot volley past Allan McGregor.
Steve Bruce was forced into a double change at half-time, with Meyler going off and McGregor replaced in goal by Steve Harper after an earlier clash with Young.
Hull started the second period as they began the first, and Yannick Sagbo tested De Gea before a Davies header went just wide.
Tom Huddlestone had a goal-bound piledriver deflected behind by Patrice Evra. The manager's son, Alex Bruce, came closest to restoring Hull's lead, hitting the crossbar with a header.
Despite all this pressure, United took the lead when Young's cross was headed past his own keeper by the unfortunate Chester, who had Rooney lurking behind him.
There was still time for some late drama. Valencia was sent off for kicking the ball away, a second bookable offence, before de Gea was forced to smother a late close-range effort from the ubiquitous Chester.
Rooney said this to Sky Sports after the game as reported by the BBC:
There were a lot of long balls to deal with in the last five minutes but we dug deep and it was a massive result for us. We started poorly today, it was poor defending. The first goal was my fault, I lost my man and we had to come back and score an early goal.
That was one of my best goals. I've not seen it back but it was a big goal for us. We had some bad results at the start of the season but we are showing our quality now, we are fighting hard and hopefully we can surprise some people now.
|Hull City vs Manchester United|
|A. McGregor||B||D. De Gea||B+|
|J. Chester||B||C. Smalling||B-|
|A. Bruce||B+||J. Evans||C-|
|C. Davies||B||P. Evra||C|
|M. Figueroa||C-||D. Fletcher||B|
|J. Livermore||B-||T. Cleverley||B|
|A. Al-Muhamadi||B+||A. Valencia||C-|
|T. Huddlestone||B||A. Young||B+|
|Y. Sagbo||B+||W. Rooney||A|
|D. Graham||B||D. Welbeck||B+|
The frantic Christmas schedule continues with both teams playing again on Saturday. Manchester United travel to Norwich, and Hull entertain Fulham.