The England striker prodded home from Raheem Sterling’s header to make it 2-1.
Liverpool’s opener was all about the pass from the Jordan Henderson as Raheem Sterling placed the ball past Fraser Forster.
Southampton pressed for an equaliser and it finally came in the second half, with Lucas caught ball watching as Dusan Tadic’s backheel was slammed home by Nathaniel Clyne.
Following the introduction of Rickie Lambert, Liverpool immediately lifted their game and minutes later it was 2-1.