The Reds looked set to be frustrated as Sunderland dug in at Anfield but Divock Origi broke the deadlock on 75 minutes before James Milner made it 2-0 in stoppage time.
After last week's goalless draw against Southampton which saw them lose top spot Liverpool's hard-earned win against a resolute Black Cats side got them back on track.
It was not the free-flowing performance which has become their trademark this season but that was partly down to Sunderland's dogged resistance and defensive set-up.
"I didn't think about Southampton for a second today," added the German when he was asked whether he felt a repeat of St Mary's was on the cards.
"No, today was much more defensive. I don't think I have ever played against a more defensive team, man-marking against Coutinho and (Victor) Anichebe left full-back.
"It is a nice thing to learn that we are able to beat even the most defensive team I ever played against."