The first real chance of the half fell to the visitors when Sebastian Larsson pulled the ball back for Stephane Sessegnon. The attacker then threaded a pass inside the area to Craig Gardner but the midfielder shot into the straight netting.
Mario Balotelli headed over for City when well placed, but despite the home side beginning to take control of the match, it was the visiting Black Cats who broke the deadlock.
Sessegnon squared for Larsson, who slotted the ball past City goalkeeper Joe Hart from 18 yards out in the 31st minute.
The Black Cats continued to look confident in possession having taken the lead, but they were pegged back with two minutes of the half remaining.
Edin Dzeko was adjudged to have been brought down inside the area and Balotelli stepped up convert the resultant penalty past Simon Mignolet.
Just as it looked as though the sides would head into half time level, Bendtner rose highest to meet a cross from Sessegnon and head the away side in front.