Second-place Tottenham is now on the back foot as it prepares to play Crystal Palace on Wednesday.
Since Chelsea lost twice in four league games, including at Old Trafford ten days ago, they have responded by reaching the FA Cup final and strengthening their grip on top spot in the league.
"Tonight it was a big win for us", Conte declared.
- Since their return to the top-flight in 2012-13, Southampton have scored more away Premier League goals at Stamford Bridge than any other side (9). I think that, in that moment, we have had a really important psychological test, and our answer was very good.
"My players showed me a great will and desire to win the game", Chelsea manager Antonio Conte said.
Chelsea's 2-1 loss at home to Palace was followed a fortnight later by their defeat to Manchester United, two results that reopened the title race and led some to wonder whether the Blues were feeling the pressure. "We are ready to fight until the end".
Eight minutes into the second 45 and Diego Costa headed past Fraser Forster to make it 3-1, later adding a second after some superb link-up play with Eden Hazard and Pedro.
The Italian said: "For strikers it's very important to score because the goal is your life".
However, Chelsea suffered a scare on 24 minutes when former Blue Oriol Romeu netted from close-range. "I'm pleased with our fantastic performance".
"We must be confident for the future. I was a footballer and I know what happens in every single player", he said.
"My choice was right for the game against Tottenham and the game today".
This was Chelsea's first home game since it was announced that John Terry would be leaving in the summer following 22 years of service.
Whether or not Costa is still a Chelsea player next season is immaterial in respect of the current campaign.
Chelsea now head the table by seven points and three of their remaining five games are at Stamford Bridge.
When you're scoring four goals in a game you might not be as concerned how many you concede as long as you win the game, but when you change to a bigger perspective, 11 games without a clean sheet is a poor, poor record for a champion-elect team. But, Costa did not just stop here as he scored another goal in the 89th minute of the match that confirmed that Chelsea will be at the top of the points table after this match.