The result left both sides on 23 points from 24 matches.
They are level with Burnley and four ahead of 18th-placed Cardiff City, after the home team’s James Ward-Prowse cancelled out Wilfried Zaha’s opener for Crystal Palace.
The lively Zaha fired the visitors ahead with a stinging low shot from inside the penalty area in the 41st minute.
He beat Southampton goalkeeper Alex McCarthy at the near post after good work by Andros Townsend.
Ward-Prowse equalised out of the blue in the 77th with a superb first-time finish from 10 metres after Matt Targett squared the ball back to the midfielder from the right flank.
The visitors paid the price for a poor finish by Mamadou Sakho several minutes earlier when his feeble close-range shot was cleared off the line by Jan Bednarek.
The Crystal Palace defender then spurned another chance shortly after the equaliser.
Zaha was sent off in the dying minutes.
This was when he received two yellow cards in quick succession, both for dissent as he clashed with Ward-Prowse and then sarcastically applauded referee Andre Marriner. (Reuters/NAN)