Soon, a well-timed pass by Jorginho played in Morata to get his second goal in as many weeks but the latter shot straight at McCarthy.
Humbly, Hazard quickly moved on to talking about his teammates and continued to shower praise on Kante: 'France won the World Cup because of N'Golo, two years ago we won the league because of N'Golo and Leicester won the league because of N'Golo.
Man of the Moment, Hazard stepped up on the half and hour mark to power home the opener after getting central with the defence.
The miss proved costly for the hosts because three minutes later - just after Chelsea had penalty appeals waved away after Wesley Hoedt brought down Giroud - Chelsea took the lead. The Spain International likes to play where there is space but Southampton wouldn't give them that luxury on Sunday.
Wesley Hoedt sent a lazy pass to Pierre-Emile Højbjerg and the Danish midfielder failed to spot Barkley in close attendance.
Hazard, who has eight goals for Chelsea in all competitions this season, opened the scoring in the 30th minute.
The Saints should have gone ahead in the 28th minute with their first chance of the game, but Danny Ings somehow placed his effort over the crossbar. Hughes's side were on the front foot at that point and there were howls of disbelief when Ings volleyed over from close range after a fine cross from Ryan Bertrand.
Hazard finished nicely after being set up by Barkley. I'm still sometimes feeling it a little bit.
The mid-table side started the second half in a positive light, with no changes at the break from neither side.
The Blues derailed their quest when Ross Barkley tap-in a free-kick by Willian for his first goal in the club's colours since arriving from Everton in January.
Meanwhile, Southampton head to the game after losing 2-0 against Wolves last weekend in the Premier League.