Sadio Mane has now scored 30 goals in all competitions for Liverpool since the start of the 2018-19 season, level with Mohamed Salah.
He scored Liverpool's second goal as they maintain a two-goal lead over Burnley in Saturday's Premier League fixture.
Four minutes after Chris Woods turned the ball to his own net to open the scoring, Mane doubled the Reds' lead before half-time.
The 27-year-old finished off a pass from Roberto Firmino with a calm right-footed shot.
The Senegalese star, who shared last season's Premier League Golden Boot with Salah and Arsenal's Pierre-Emerick Aubameyang, is now the joint-top scorer for Liverpool across all competitions since August 2018.