Brentford made an early comeback via a brilliant volley from Vitali Genault, but an unfortunate goal from goalkeeper Alvaro Fernandez gave Southampton a halftime lead.
Southampton took both Armando Broza and Che Adams on target in the second half as Ralph Hasenhuetl's side won the league for the first time this season by more than a goal margin.
It was only Southampton's third home win of the season and it lifted them above Brentford to 11th place with 24 points.
Brentford slipped to 13th place with 23 points.
"We have scored four goals at home for the first time since November 2017," Hasenhuetl, whose team is unbeaten in four league games, said.
"It's not very often that injury time runs out and we feel comfortable because sometimes it's tight here. We did a great job today."
The event was scheduled to take place on December 18, but fell victim to a surge in COVID-19 infections.
The club has since been bought by Sport Republic, a London-based investment firm backed by billionaire Solak, and on Tuesday the mood was encouraging on the south coast.
Bednarek had to get his head around a typically pinpoint delivery by James Ward-Prause in the fifth minute to give the hosts the launchpad for a live performance.
Brentford, however, did not deter, and equalized in surprising fashion, as Genault volleyed to the left foot from a brilliant cross by Brian Mbumo.
Southampton poked their noses again after 37 minutes in unusual fashion.
As a corner was cleared to Ibrahima Diallo on the edge of the penalty area, he was given too much time to deliver a bouncing shot that hit the post but rebounded from behind goalkeeper Fernandez's hand.
Albanian forward Broja, on loan from Chelsea, made it 3–1 in the 49th minute when he was played through by Oriol Romeu and managed to squeeze his shot to Fernández for his fifth Premier League goal of the season. Stayed.
Brentford's defense was then caught in sight of the ball as a long punt forward was well controlled by Adams who beat Fernandez with 20 minutes to go.
It was a disappointing night for Brentford, who impressed during his inaugural Premier League season, scoring four goals for the first time this season.
"Fair play for Southampton but my job is to see my team's performance. If we're not playing 100% every second of every Premier League match we're not getting anything out of it," manager Thomas Frank said.
"We needed to do better 2-1. We can't give away three goals, especially the last two."