Sir Alex Ferguson's men came from behind twice in Germany as the England star inspired a superb comeback in the latter stages, with Javier Hernandez also on target for the visitors
Sir Alex Ferguson's team were made to work hard for victory after Artur Sobiech, Karim Haggui and Mohammed Abdellaoue sent the hosts into a 3-1 lead, with Javier Hernandez grabbing the Red Devils' first goal after Sobiech's opener.
Wayne Rooney converted both a free-kick and a penalty to draw United level before new signing Shinji Kagawa completed the turnaround late on.
Ferguson picked an attacking line-up for the game with Kagawa, Rooney, Hernandez, Ashley Young and Nani all starting for the visitors, who had drawn a blank in their two previous pre-season matches.
Perhaps unsurprisingly then, United started on the front foot although it took almost 20 minutes before the Premier League runners-up managed to create a clear-cut chance.
It came via Ashley Young who managed to beat Henning Hauger and find Nemanja Vidic completely unmarked in the box, but the skipper could only send his effort sailing high over the bar.
Minutes later, teenager Michael Keane squandered two chances to put his team ahead. Firstly he failed to hit the target after picking up a cut-back from Kagawa before missing from close-range seconds later with goalkeeper Ron-Robert Zieler out of his goal.
The chances wasted were to prove costly as mid-way through the first half the hosts took the lead. Anders Lindegaard could only fumble a shot from Jan Schlaudraff leaving Sobiech to finish smartly from close range for the opener.
Hannover's celebrations were short-lived, however, as six minutes later the visitors were level. A fierce shot by Rooney was only parried by Zieler and Hernandez was on hand to tap home the equaliser.
Chances continued to come in an entertaining first half with Cleverley and Kagawa both testing Zieler with strong shots but neither were able to beat the Hannover goalkeeper who ensured the teams went in at half-time level.
Both teams made changes at the break and they proved effective for the hosts who went back in front within minutes of the restart.
When substitute David de Gea could only punch clear from a corner, the ball was swung back into the area for Haggui to head strongly past the Spaniard to put Hannover back in front.
Back came United, with Hernandez almost grabbing his second equaliser 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 were then relieved after the referee waved away Hannover appeals for a penalty. A surging run by Steve Cherundolo was rudely interrupted by Cleverley who left the captain on the floor and appealing to the official, but he ignored the home side's claims and United escaped.
It was only a temporary reprieve as five minutes later Abdellaoue was on hand to give the hosts 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 effort 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 Rooney again who pulled United level. A defence-splitting pass by Nani sent the striker running clear on goal and after he took the ball around Zieler, the goalkeeper could only pull him down leaving the referee no option but 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 visitors the lead for the first time in the match and secure a 4-3 win.