Sir Alex Ferguson's men came from behind twice in Germany with Javier Hernandez also on target, with Rooney hugely influential for the Red Devils.
A series of early Manchester misses proved costly as midway through the first half the host took the lead. Anders Lindegaard could only fumble a shot from Jan Schlaudraff, leaving Artur Sobiech to finish smartly from close range for the opener.
Hannover's celebrations were short-lived, however, as six minutes later the visitor was level. A fierce shot by Rooney was only parried by Zieler and Hernandez was on hand to tap home the equalizer.
Both teams made changes at the break and they proved effective for the host, which went back in front within minutes of the restart. Three minutes in and substitute David de Gea could only punch clear from a corner. The ball was swung back into the area where Karim Haggui headed strongly past the Spaniard to put Hannover back in front.
Back come United, with Hernandez who almost grabbed his second equalizer of the game. The Mexican did superbly to create a chance for himself but his shot was tipped away to safety by Zieler.
Ferguson's side was then relieved after the referee waved away Hannover appeals for a penalty. A surging run by American international Steve Cherundolo was rudely interrupted by Cleverley, who left the Hannover captain on the floor and appealing to the official. But the ref ignored the home side's claims and United escaped.
Yet it was only a temporary reprieve as five minutes later Mohammed Abdellaoue was on hand to give the host a two-goal lead with a sumptuous finish. The forward latched onto a pass from Lars Stindl, and, with his back to goal, backheeled the ball past De Gea to make it 3-1.
The goal spurred United into action and minutes later Rooney had reduced the deficit. United won a free kick on the edge of the area and the England international curled a gorgeous shot over the wall and into the bottom corner of Zieler's goal with the goalkeeper a spectator.
Hannover continued to press but with just 10 minutes to go it was that man Rooney again who pulled Manchester United level. An defense-splitting pass by Nani sent the striker running clear on goal. Rooney took the ball around the goalkeeper, who pulled him down, leaving the referee no option to point to the spot. Rooney picked himself before calmly slotting home, sending the goalkeeper the wrong way with his second of the night to make it 3-3.
There was still time for more goals, however, and Rooney was again involved as United took the lead. The striker nodded a long ball into Kagawa's path and the Japan international struck a fierce shot across goal to give the visitor the lead for the first time in the match and secure a 4-3 win.
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