Substitute Enner Valencia scored his first Everton goal to break Southampton's resolve and send the home side on their way to a 3-0 win at Goodison Park on Monday, with Leighton Baines and Romelu Lukaku also finding the net.
Valencia had not scored in the Premier League since getting two goals for West Ham United against Manchester City last January, but secured the breakthrough in the 73rd minute when he bundled home the rebound after Fraser Forster had saved Lukaku's header.
Ronald Koeman's side had struggled to find solutions to prise open his former employers but killed off the contest in the 81st minute when Baines beat Forster from the spot after Maya Yoshida clumsily brought down Lukaku.
Everton ran riot as Southampton crumbled and Lukaku signed off a dominant second half when he slammed an emphatic effort into the top corner from just inside the visitors' box in the 89th minute.
The win keeps Everton in seventh on 30 points, six behind Manchester United who play later on Monday, while Southampton remain on 24 points.
(Reporting by Ed Dove; Editing by Clare Fallon)