A minute later, Hannover punished United's profligacy as Jan Schlaudraff's shot was spilled by Anders Lindegaard, allowing Sobiech to nip in and lift a neat finish over the scrambling Dane.
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