Ben Mee gave the hosts the lead when he met Brian Mbuemo’s cross with a sharp header in the 41st minute.
And three minutes later, Brentford doubled their lead after Mbuemo fired into the bottom corner.
Mathias Jensen added a third goal with nine minutes remaining, heading in Rico Henry’s pass from close range.
Meanwhile, Brentford extended their unbeaten run to nine matches, the longest run in the top flight for 87 years.
Bees, the pride of west London, know who they are
Brentford’s win lifted them above Fulham – and they were already ahead of another west London team.
The Bees, unbeaten in the league since October 23, have always looked the better of their opponents and are now just six points off the top four.
Thomas Frank’s side almost took the lead in the 8th minute when Wissa rounded Southampton goalkeeper Gavin Bazuna and hit the crossbar from a tight angle.
And after a series of half-chances, the hosts did take the lead through Mee’s header, with the defender rising higher to meet Mbuemo’s inviting cross.
Mee was checked for concussion immediately after his opener collided heads with a Saints defender but was able to continue as the Bees doubled their lead through Mbuemo.
Brentford’s top scorer Ivan Toney cleared a shot off the line midway through the second half before Jensen completed the win with a header into the far corner.
Southampton are still at the bottom
Southampton may have given Newcastle a scare in the Carabao Cup semi-final on Tuesday, but they looked composed against Brentford.
The visitors went close when James Ward-Prowse fired home early in the first half, but the midfielder decided to tip the ball just beyond the reach of team-mate Che Adams when the shot looked better.
In the second half, substitute Theo Walcott had a decent shot blocked by the combination of Ethan Pinnock and Mads Roerslev to make it 2-0.
But Saints manager Nathan Jones will be most concerned about the defence.
Southampton have conceded 53 goals in their last 27 Premier League games, keeping just one clean sheet in that time, and Brentford have repeatedly opened the scoring.
The Saints are still stuck at the bottom of the table as they look to improve a run that has seen them lose four of their last five games.
They face Wolves next Saturday, while Brentford face leaders Arsenal on the same day.
