Costa's two goals were his first in eight matches - a barren run which has coincided with reports that the striker is keen to make a big-money move to China.
"Today I have to be pleased with the effort of my players". Eden Hazard and Diego Costa played very well.
Chelsea playmaker Eden Hazard says he is only focused on finishing the season on a high and is not thinking about his long-term future.
Costa, who has been misfiring of late, took his chance in the 53rd minute and powered in a header - his 50th Premier League goal - after a corner and one-two between Fabregas and Hazard.
Chelsea are four points clear of second-placed Spurs with six league games remaining.
Hazard, Costa and Cesc Fabregas returned to the Chelsea XI after starting Saturday's 4-2 win over Tottenham on the bench and they combined for the fifth-minute opener. The goalkeeper parried the shot but the ball fell to Romeu for a simple tap-in.
There was still time for Chelsea to concede a second as Cedric Soares' cross was headed in by ex-Blues man Bertrand.
"For this reason I want to say thanks to our fans because they showed great passion and pushed us a lot".
Set-pieces continued to prove the home side's Achilles heel, with Courtois obliged to swat away a risky Ward-Prowse free-kick before Sofiane Boufal thrashed into the side-netting at a corner.
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It's likely that one of Terry's last acts of a 22-year association with Chelsea will be to lift the Premier League trophy. You reach the final in the FA Cup, a great competition. It paid off at Wembley and the effects were felt by Southampton as the refreshed duo unsettled the Southampton defence.
However speaking after the victory on Tuesday Conte said he believes his choices were correct.
But Conte resisted the temptation on Monday to taunt his rival, which has won seven league games in succession to put pressure on the Italian's league leaders.
The contribution of Fabregas shouldn't be overlooked.
Costa would not be denied the next time he got a sight of goal in the 53rd minute as he brought up a half-century of league goals on his 85th appearance since signing from Atletico Madrid in 2014.
Chelsea and Tottenham were the visitors on Saturday evening, whilst Manchester City faced Arsenal the following day.
Conte, after helping Chelsea recover from its loss to United in the previous round, now takes his team back to northern England to face Everton.
Chelsea boss Antonio Conte: "We passed a big step, a big psychological step after the defeat against United".
But Conte reckons players can only be great by playing as part of a team.
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