The hosts started in superb fashion as Chester's close-range volley and a deflected effort from David Meyler established a two-goal advantage inside 15 minutes, but Chris Smalling and Wayne Rooney netted to level proceedings.
The Tigers had opportunities through Danny Graham and Alex Bruce in the second half, but were made to rue missed chances as Chester went from hero to villain, heading Ashley Young's cross past his own goalkeeper.
Bruce refused to blame the centre-back for the costly error and is confident the 24-year-old - who used to play for the Red Devils - will learn from the mistake.
"James Chester was a young player at Manchester United and when he scored he was in dreamland, and he had a chance at the death to get a result," Bruce told BBC Sport.
"He put one in his own net. We've all done it and he'll have to live with that but he'll get over it because he's a very good young player."
Hull had only conceded three home goals in the Premier League before the meeting with United, but Bruce felt his players were punished for errors at both ends of the pitch against his former club.
He added: "Over the years I've been close a few times to beating them but never 2-0 up against them within 15 minutes, and the one thing we've been able to do since I've been here is hold a lead.
"We made too many mistakes at crucial times. We created umpteen opportunities in the second half but we made mistakes and you get punished against a team like Manchester United."