Danny Ings scored his 19th league goal when he corralled Stuart Armstrong’s intended pass before flicking the ball into the net to give Southamtpon a deserved 1-0 lead on 31 minutes.
But Richarlison cancelled out Southampton’s lead after Lucas Digne picked out the forward with a through ball that split the defence and allowed the forward to fire past Alex McCarthy.
Alex Iwobi forced McCarthy into a point-blank save from the right side of the box on 23 minutes, which was the best chance for either side in the early stages.
Jordan Pickford then took no chances and pushed James Ward-Prowse’s free kick over the bar and from the ensuing corner, Ings rattled the post.
Ward-Prowse would draws a penalty on a clumsy foul from Andre Gomes, but the midfielder can’t convert from the spot, thrashing his effort against the bar.
Southampton, however, took the lead when Ings managed to control the ball and steer it goal-bound to reward the visitor’s efforts.
Richarlison equalised just over 10 minutes later, with Everton being in the ascendancy ever since Southampton took the lead.
Everton: Pickford, Digne, Keane, Mina, Coleman, Gordon (Bernard 74), Davies, Andre Gomes (Sigurdsson 42), Iwobi (Sidibe 45), Richarlison, Calvert-Lewin (Kean 68)
Unused subs: Stekelenburg (GK), Baines, Walcott, Branthwaite, Baningime
Goals: Richarlison (43)
Bookings: Richarlison (45), Digne (90+1)
Southampton: McCarthy, Bertrand, Bednarek, Stephens, Walker-Peters, Romeu (Hojbjerg 70), Ward-Prowse, Redmond, Armstrong (Smallbone 88), Adams (Long 70), Ings
Unused subs: Gunn (GK), Jankewitz, Ferry, Obafemi, Danso, Smallbone, Vokins
Goals: Ings (31)
Bookings: Armstrong (14), Stephens (34), Bednarek (60)