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.
1. 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.
2. 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.
3. Ben White 7-10
The former Southampton academy graduate kept another, in Nathan Tella, quiet throughout and often nullified any Southampton threat.
4. 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.