Liverpool started the game brightly with chances for Krisztian Nemeth and Daniel Pacheco but were a goal down just before the half hour mark when Godwin Antwi put through his own net.
It was 2-0 eight minutes before half time and was almost worse, Gary Mackay-Steven clearing another shot off the line.
The Reds tried to get back in the game in the second half but it was Sunderland who looked more likely to score the next goal and only a good display from captain Stephen Darby prevented them from doing so.