The Blues were ruthless against their opponents with Eden Hazard and Diego Costa both on the scoresheet for Antonio Conte’s side.
And Cahill was pleased with the way his Chelsea team-mates dealt with an impressive Saints team at St Mary’s.
He said: “Southampton’s record at home is very good – we knew that. But we knew if we carried on our form, we’d cause them problems. We worked hard.
“It’s too early in terms of any team talking about winning the [Premier League]”
Chelsea defender Gary Cahill
“Four wins in the league now, four clean sheets – we keep going.
“We need those types of [attacking star] players who can turn the game in a moment. It’s a pleasure to have these guys in the side.
“It’s too early in terms of any team talking about winning the league but its important to stay near the top.
“We want to be up and among it. I can’t see anyone running away with it this season.”
The result means Chelsea move up to fourth and are now just one point off the top of the table.