Buoyant Chelsea extended their Premier League lead and calmed nerves at Stamford Bridge with a 4-2 win over Southampton on Tuesday that moved them seven points clear of their nearest pursuers Tottenham Hotspur.

Goals from Eden Hazard, captain Gary Cahill and two from a buzzing Diego Costa ensured Chelsea stayed on course for the double after they beat Tottenham by the same score in their FA Cup semi-final at Wembley on Saturday.

The victory pushed Chelsea on to 78 points after 33 games and exerted more pressure on second-placed Spurs, who must win a potentially awkward London derby at Crystal Palace on Wednesday to restore the gap to four points.

“We had a really important psychological test and our answer was good,” manager Antonio Conte said. “We have reached the final of the FA Cup but the other competition is totally open. But we fight until the end.”

Conte juggled his team again on Tuesday starting with Costa and Hazard, who came off the bench at Wembley, and his tactics were rewarded.

It took them less than five minutes to open a lead when Costa controlled a pass from Cesc Fabregas, surged forward and cut the ball back for the advancing Hazard, who angled his shot into the bottom corner of Fraser Forster’s net.