Steve Bruce's side raced to an early lead, with former United defender James Chester volleying in Alex Bruce's knock-down from close range, before the home side doubled the lead through David Meyler, his limp shot taking an unfortunate deflection off Jonny Evans and trickling in.
United came roaring back, with Rooney instrumental. The forward's inch-perfect free kick was headed into the back of the net by Chris Smalling and moments later the 28-year-old saw his stunning volley fly past Allan McGregor to level the scores.
The Tigers regrouped at halftime and could have re-taken the lead when Bruce smashed the crossbar. However, having opened the scoring, Chester went from hero to zero as he headed past his own keeper to give the Red Devils the lead and the victory - despite Antonio Valencia receiving a red card late on.
Hull named the same side for the fourth straight match, while David Moyes included Darren Fletcher in the United starting XI for the first time in over a year. Michael Carrick, meanwhile, was fit enough for a place on the bench after overcoming injury.
The home side stormed into the lead as early as the fourth minute. Tom Huddlestone's corner was headed back across goal by Bruce and Chester was on hand to volley home from close range. However, replays suggested a corner should not have been awarded as Ahmed Elmohamady had kicked the ball straight out of play.
Hull doubled the advantage just nine minutes later to leave the home supporters in dreamland. A bout of pinball in the United box resulted in Meyler's goalbound effort deflecting off Evans and deceiving goalkeeper David de Gea.
United needed a swift response and duly delivered after 19 minutes. Substitute Adnan Januzaj tricked his way past Maynor Figueroa to win a free kick and Rooney's testing set piece was powered into the back of the net by Smalling.
The visiting side twice came close to leveling with a Danny Welbeck header and Tom Cleverley's long-range strike and the pressure was rewarded when Rooney played a one-two with Welbeck before teeing himself up for a volley that he rifled into the top corner from 25 yards.
Hull was forced into a change at halftime with goalkeeper Allan McGregor - who was involved in a first-half collision with Ashley Young - being replaced by Steve Harper.
The home side twice forced good opportunities in the early stages of the second half. First Yannick Sagbo had an effort beaten away be De Gea before Curtis Davies glanced Huddlestone's corner wide. Bruce came even closer just after the hour mark when his header rebounded off the crossbar.
United punished Hull for its profligacy in the 66th minute, though, as Young got past Figueroa and whipped a ball into the box that Chester headed past substitute goalkeeper Harper when under pressure from Rooney.
Hull pushed for a leveler in the closing stages and Danny Graham should have done better with a tame back-post header.
Valencia added to the tension in injury time when his petulance in kicking the ball away earned him a second yellow card, and Chester almost redeemed himself but saw his late toe-poked effort smuggled to safety by De Gea.