Liverpool bounced back after their home loss to Manchester City.
Virgil van Dijk got on the end of Mohamed Salah's corner and headed the ball past a Sunderland defender into the net; it was the only goal of the match.
Shortly afterwards, Liverpool midfielder Wataru Endo was injured and had to be carried off on a stretcher. The Japanese player held his hands in front of his face as he was carried away and appeared to be in considerable pain.
Liverpool are sixth in the table, Sunderland 11th.
Earlier on Wednesday, Manchester City beat Fulham 3-0. With one more game played, they are now three points behind Arsenal, who top the table.
Third-placed Aston Villa held on to third place with a 1-0 home win over Brighton.
