Danny Welbeck put the Seagulls ahead inside the first two minutes and an own goal from Mohammed Salisu a minute before halftime looked to put the hosts on control.
Southampton fought back through James Ward-Prowse as the midfielder scored either side of halftime to put Saints on level terms.
Story of the match
Welbeck took full advantage as he prodded the ball home from a couple of yards away for his fourth of the season and the first goal at home for the Seagulls since January 18th. It was the fastest goal in Brighton's Premier League history.
Southampton nearly leveled in the 13rd minute as Tino Livramento's drive hit the post and bounced out off of Rob Sanchez, Che Adams failing to stretch far enough to poke home.
Moments later, it would be two as Welbeck turned provider, picking out Trossard in space and his return diagonal pass was cut out by Salisu, who accidentally put it in his own net.
Saints responded in stoppage time as Nathan Tella drew a foul on Cucurella and Ward-Prowse bent the ensuing free kick in and off of the post with his right foot.
Nine minutes into the second half, the visitors were level. Tella won the ball back, Romeu played a cheeky backheel to Ward-Prowse and the midfielder tucked his shot inside the left post from 20 yards out.
Sanchez was then called on to save at full stretch from Shane Long and at the other end, Forster held onto Solly March's low drive.
Gross thought he had sealed all three points for Brighton late on with a goal into the bottom corner, but VAR ruled he was offsides by inches as the match concluded as it began.
Man of the match: James Ward-Prowse
The Southampton skipper scored the way he usually does: off of set-pieces. His first came with a slice of luck, but his second was a peach of a goal.