Chelsea overcame Watford 2-1 in the late kick-off thanks to a double from Eden Hazard.
Hazard rounded goalkeeper Ben Foster in first-half stoppage time to put the Blues in front before Roberto Pereyra scored a superb equaliser two minutes later.
But the Chelsea playmaker restored the visitors' lead from the penalty spot in the 58th minute after he was fouled by Foster.
Alvaro Morata missed out again as Chelsea named an unchanged line-up from their Leicester defeat for the Premier League clash at Watford.
Spain striker Morata was expected to recover from a knee injury for the Vicarage Road trip but was once again not named in Chelsea's match squad.
Sarri kept faith with the same side that slipped up 1-0 at home to Leicester on Saturday, with Eden Hazard again employed as a 'false nine'.
Watford also named an unchanged starting XI, following on from their 2-0 win at West Ham on Saturday.
Watford and Chelsea went in level at 1-1 at half-time following two stoppage-time goals.
Eden Hazard latched onto a Kovacic through ball and rounded Hornets goalkeeper Foster to open the scoring with his 100th Blues goal in the first minute of added time.
But just two minutes and 17 seconds later the hosts levelled when Pereyra volleyed home from the edge of the box from a Jose Holebas corner.
Hazard restored the visitors' lead from the penalty spot 13 minutes into the second period.
The Belgium international sent Foster the wrong way from 12 yards after being brought down by the keeper.
Watford were denied a spot-kick of their own minutes earlier when Gerard Deulofeu went down in the box following a tangle with Blues defender David Luiz.
Sarri's side held on to their 2-1 advantage as they bounced back from the weekend loss to Leicester.
The victory moved Chelsea back above Arsenal and into fourth spot, four points behind third-placed Manchester City and 11 behind leaders Liverpool.
Blues midfielder N'Golo Kante had a good chance to make the result more comfortable, while Watford, who finished the day in ninth position, created little in their search for a second equaliser.