Liverpool had the better of the possession during the opening 45 minutes, although they found goalscoring chances hard to come by.
After Jack Colback had gone close shortly after the restart for Sunderland, Bendtner's winning strike arrived in the 56th minute.
Fraizer Campbell's initial effort struck the post, before hitting Liverpool goalkeeper Pepe Reina on the back. The ball rebounded off the woodwork again and Bendtner reacted quickest to score from close range.
Liverpool manager Kenny Dalglish responded by introducing captain Steven Gerrard and Andy Carroll into the action, but the attacking duo were unable to inspire their side to find an equaliser.
The Reds have now lost four of their last five away matches in the Premier League.