The return of some fans at Brighton for the first time since February saw them go ahead with a well-taken first half penalty from Pascal Gross.
A towering header from Vestergaard from a James Ward-Prowse corner pulled the Saints level and Danny Ings' second half spot kick ensured the Saints secured all three points.
It was tough on Brighton and their fans as VAR ruled that Solly March's 80th minute challenge on Kyle-Walker-Peters was inside the box.
Ings, in his first game back from a knee injury, showed little sympathy and sent Maty Ryan the wrong way from the spot.
Scroll down and click through to see how the players rated.
9. Solly March 6/10
Had played quite well and harsh to award the late penalty against him. Worked hard down the left and delivered some nice crosses. Wasted a good chance in the second half when he sliced wide when well placed.
10. Danny Welbeck 6/10
A good display from Welbeck, especially in the first half where he linked the play well and showed he still has plenty of pace. Faded after the break after a few whacks from Bednarek
11. Aaron Connolly 6/10
Played a big part in the penalty when his flick was handled by JWP. Dangerous in the first half but replaced by Maupay on 64 minutes. No sulking about being substituted this time
12. Neal Maupay 5/10
Replaced Connolly on 64 minutes but rarely troubled the Saints rearguard. A smart turn and shot just wide late on