The Polish striker narrowly failed to convert another close-range opening two minutes later, pressured well by Patrice Evra, but the hosts' time in the ascendancy was short-lived as United drew level just after the half-hour.
Evra surged down the left flank and released Nani, whose pull-back fell neatly for Rooney. The striker's swept shot was parried away by former United goalkeeper Ron-Robert Zieler, but only as far as Chicharito, four yards out, who used a neat touch to control and a simple tap-in to draw the Reds level.
The visitors might have been in front by the interval, but Nani blazed over after a neat free-kick routine, Cleverley fired straight at Zieler after clever approach work and Kagawa had a pair of shots blocked by the alert Avevor.
However, Hannover's dormant threat briefly emerged when Lindegaard plunged to sharply save from Konstantin Rausch, and the Bundesliga side forged ahead for a second time shortly after the commencement of the second half.
David De Gea and Ryan Giggs were introduced at the expense of Lindegaard and Young during the interval, and the former's first involvement was to punch clear a corner. With play ongoing, the ball was lifted back into the area and Karim Haggui rose highest to thump home a header.
The Tunisian international was one of eight substitutes brought on by the hosts and another, Didier Ya Konen, twice brought sharp saves from De Gea after the interval. United might have levelled when Rooney released Chicharito, but Zieler did brilliantly to fend away the Mexican's effort with his right foot.