Trossard struck in the 56th minute after superb build up play from Adam Lallana and Danny Welbeck.
Skipper Lewis Dunk had earlier given Brighton the lead with a thumping first half header from Pascal Gross' corner but that was cancelled out when Saints striker Che Adams lashed home his third goal in three matches.
Victory for Graham Potter's injury hit Brighton lifts them three points above the drop zone while Southampton are 14th.
Scroll down and click through to see who shone and who struggled for Potter's men at St Mary's.
Victory for Graham Potter's injury hit Brighton lifts them three points above the drop zone while Southampton are 14th.
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Leandro Trossard celebrates his third goal of the season and the winner against Southampton
. Robert Sanchez 9-10
Sanchez’s strong attributes were on show once again in Southampton as he was quick off his line on more than one occasion while producing some fine saves. Helpless to Adams’s equaliser as the striker fired home a volley from close range.
. Joel Veltman 7-10
Another strong performance from the Netherlands international. Was required to swap to left-back at half-time but never looked out of place while dealing with the threat of Nathan Redmond superbly.
. Ben White 7-10
The former Southampton academy graduate kept another, in Nathan Tella, quiet throughout and often nullified any Southampton threat.
. Lewis Dunk 10-10
A true captain’s performance. Dunk commanded the backline excellently and was on the end of any crosses to divert the danger. Of course his shining moment came when he rose above Ryan Bertrand to head home from a corner.
9. Leandro Trossard 8-10
After a relatively quiet first half, Trossard made amends by scoring the winner. A well-worked team move saw Lallana and Welbeck combine to slot him behind the Saints backline before the Belgian did the rest
10. Danny Welbeck 8-10
Perhaps not Welbeck's busiest afternoon in front of goal, but the England international laid the groundwork and worked tirelessly off the ball. Provided the assist to Trossard’s winner and consistently showed his quality on the ball.
11. Neal Maupay 7-10
Maupay operated slightly wider than usual, and in doing so, produced one of his best performances in recent weeks. Will be frustrated not to get on the scoresheet as he was often denied by Fraser Forster, but his well-struck effort forced the corner to which Brighton gained the first advantage.
12. Andi Zeqiri 7-10
On for Dan Burn and the striker filled in well at left wing back. Lively.