Sunderland played the last 40 minutes with 10 men after the sending-off of Liam Bridcutt and the result left Liverpool eighth and Sunderland 15th.
Liverpool have now lost just one match in their past 13.
"We've still got a way to go, but the exciting thing is that in my two years here we've always been better in the second part of the season, that's the business end," said manager Brendan Rodgers.
"We've still got (Daniel) Sturridge, (Raheem) Sterling, (Adam) Lallana and (Glen) Johnson to come back into the squad.
"It's going how I hoped it would and hopefully we can continue with this momentum."
Sunderland manager Gus Poyet said his men were not ambitious enough on the day.
"We did practically nothing in the first half apart from wait for Liverpool to score," he said.
"Then we had a go."
West Brom moved out of the bottom three with a 1-0 win over Hull, while West Ham were held to a 1-1 draw at Swansea in the other afternoon game.
-AAP