The Blues continued bossing the game nearly exclusively but would have to wait until the final two minutes of the 90 to get their fourth, although it was worth waiting for as Costa showed sublime feet to skip past half the Southampton team before arrowing his shot into the back of the net.
Antonio Conte said his team selection at Wembley had been justified after Chelsea beat Southampton 4-2 at Stamford Bridge.
Cahill missed his side's FA Cup semi-final victory over Tottenham with an illness, while Courtois recently suffered an ankle problem. "I think that, in that moment, we had a really important test, psychological test, and our answer was very good".
He told Sky Sports: "Today I have to be pleased with the effort of my players". But we must think this race is open. I'm not sure the result was ever going make a difference as to where the Premier League title ultimately ends up.
"Without (Kante) for Chelsea it's hard and the same with Romeu, it's hard for us without him".
"It's normal we have to push to try to keep this position until the end".
Conte praised the Spanish international's attitude and workrate.
Costa made it 4-1 with a delightful goal in the 89th minute, swapping passes with first Hazard and then substitute Pedro before drilling a low shot past Forster.
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And Saints boast Manolo Gabbiadini, who Chelsea boss Antonio Conte says has one of the world's best left foots. Goals are your life. I was pleased for his performance. He always worked for the team. "If my goals help the team to win the games I'm happy". Now he must continue.
If Tottenham do not manage to get a win, the race for the title will nearly definitely be over, considering there will be only five matches remaining.
"We've got six very hard games home and away so we'll do everything we can to get as high up the league as we can".
Three games in eight days follow, at home to relegation-threatened Middlesbrough, at West Brom and against the Baggies' fellow mid-table side Watford at Stamford Bridge. "I don't want my club to one day buy me a selfish player, never".
"I know if I kick the ball then probably the referee sends me off".
Three of the goals tonight came from corner situations, the joint-most of any Premier League game this season (also Man Utd v Leicester in September).
But despite claims his players lack the killer instinct required to lift major silverware, the Argentine coach remains convinced they are mentally strong enough to break the trophy drought.
Liam is ESPN FC's Chelsea correspondent.





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