The Saints have beaten Carlo Ancelotti's side 2-0 at St Mary's Stadium.
Southampton took the lead in the 27th minute when James Ward-Prowse played a neat one-two with Danny Ings, who provided the through ball for his fellow Englishman to fire a shot past Jordan Pickford.
Ings turned provider again eight minutes later when he crossed from the left flank to find Che Adams at the far post and the unmarked striker took his time to pick his spot to beat Pickford with a strike that deflected off Gylfi Sigurdsson.
With about 20 minutes to go, Everton were reduced to 10 men when defender Lucas Digne was sent off for a straight red card after he fouled Kyle Walker-Peters and Ancelotti could not bring on another defender having already made three substitutions.
Everton remain top of the standings with 13 points and a healthier goal difference than city rivals Liverpool while Southampton moved up to fifth.