Liverpool needed a late own goal to rescue a point after Sunderland threatened to pile even more pressure on head coach Arne Slot at Anfield.
Sunderland took a deserved lead after 67 minutes when Chemsdine Talbi’s 25-yard shot deflected off Virgil van Dijk and beyond the reach of Alisson.
Sunderland had already raised the warning signals – as Alisson was fortunate to turn Trai Hume’s shot on the bar in the first half before Omar Alderete headed against the post after the interval.
Slot once again left Mohamed Salah on the bench after Sunday’s win at West Ham United, but brought the Egyptian on at the start of the second half to try to bring spark into a lifeless Liverpool performance.
Alex Mac Allister had hit the woodwork in the first half with a rare Liverpool threat and it took a fortuitous own goal to avoid another damaging defeat when Florian Wirtz’s shot was deflected in off Nordi Mukiele with nine minutes left.
Sunderland almost snatched victory in stoppage time when substitute Wilson Isidor raced clear but Federico Chiesa got back to clear his shot off the line.