Everton went ahead in the ninth minute when Seamus Coleman burst into the area and finished with a powerful strike.
Saints substitute Gaston Ramirez equalised in the 71st minute, beating Toffees goalkeeper Joel Robles, who it appeared should have done better in his attempt to save the effort, with a shot from distance.
The three points mean Roberto Martinez's side are - for a few hours at least - up a place to fourth in the table, while Southampton remain ninth.
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One of Clandon Park's most historically important rooms has survived the fire that gutted the rest of the 18th century mansion.
The party has suspended Robert Blay. He was caught on camera saying he would shoot Ranil Jayawardena, his North East Hampshire rival.
Wednesday lunchtime's weather for the east of the region