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Hazard has started on the bench for Chelsea's opening two games of the Premier League season after the Belgium playmaker only returned to training earlier this month following the World Cup.
Sarri's side have maximum points from their opening two games under the Italian, but made life difficult for themselves after racing into a 2-0 lead inside 20 minutes.
Out-of-form striker Alvaro Morata scored only his second league goal of 2018, fed by a through ball from Cesar Azpilicueta 11 minutes later.
He won the 2016-17 Premier League title with Chelsea but has not started a match under new manager Maurizio Sarri this season.
The future of Hazard, who only returned to training with his club a week ago after helping Belgium finish third at the World Cup, may not be sorted out until August 31.
Chelsea manager Maurizio Sarri got off to a winning Premier League start as new signing Jorginho slotted home coolly from the penalty spot in a 3-0 win at Huddersfield on Saturday.
Sarri believes Hazard is happy and does not have the same personal reasons as Courtois to move to Real Madrid.
In a summer dominated by big moves for goalkeepers, Chelsea rushed through a deal for Kepa, 23, after Thibaut Courtois joined Real Madrid for a reported 35 million euros.
A frantic 48 hours in the transfer market provided Chelsea with a timely lift after last weekend's Community Shield defeat to Manchester City.
The 24-year-old Kovacic was part of Croatia's run to the World Cup final, where it lost to France. Kovacic has been at Madrid since 2015, joining from Inter Milan.