James Chester and David Meyler fired the Tigers 2-0 ahead inside the opening 13 minutes but United were quickly back on level terms thanks to Chris Smalling and Wayne Rooney.
Hull regrouped at half-time and nearly went in front again when Alex Bruce crashed a header against the crossbar, leaving United to claim victory thanks to Chester's own goal.
Bruce was proud of his team's performance but frustrated with the soft goals they gave away.
He told Sky Sports: "We pride ourselves on not giving anything away and unfortunately today we made too many mistakes.
"We made elementary mistakes and then all of a sudden it isn't your day, when it could have been because we had the opportunities and attempts.
"We got off to a great start but we just needed then to keep the ball better. All credit, though, we stuck at it and on another day we might have got the result.
"We've had three or four opportunities to get the next goal in front and they are the defining moments in the game, and unfortunately they've gone down the other end and we've made a mistake and they've punished us.
"Against all the big teams we've played, we've been like that, and that's the way we'll continue."