Richarlison's early strike was enough to guide Everton to only their sixth home win of the season as Southampton's alarming slump continued with a 1-0 defeat at Goodison Park.
Everton took the lead inside the opening 10 minutes as Richarlison continued his rich recent vein of form in front of goal with his third goal in three games.
Southampton left it late to muster any kind of response but could have snatched a point had Moussa Djenepo not blazed wide, or had Jannik Vestergaard managed to bundle the Saints' first attempt on target past Jordan Pickford in the final minute.
But Everton held on to secure back-to-back league wins for the first time since Boxing Day as Carlo Ancelotti's side ended a three-game home losing streak to move level on points with Liverpool and to within two points of the top four.
For Ralph Hasenhuttl and Southampton, their table-topping early-season form is a distant memory after succumbing to an eighth Premier League defeat in nine which leaves them 14th, seven clear of the relegation zone and looking over their shoulders.
