Former Everton and Watford winger Gerard Deulofeu pulled one back for Udinese before Mason Mount wrapped up Chelsea’s win late on.
Elsewhere, Dwight McNeil shone on his debut as Everton beat Dynamo Kyiv.
McNeil, who joined the Toffees from Burnley for £20m earlier this week, struck twice after coming off the bench to seal a 3-0 win for Frank Lampard’s side at Goodison Park.
Having been introduced just after the hour mark, McNeil rifled home on 73 minutes before bagging his second five minutes later after being set up by fellow debutant Ruben Vinagre.
Dominic Calvert-Lewin put Everton ahead after five minutes when he slotted home after being picked out by summer signing James Tarkowski.
At Stadio Friuli, Kante marked his return to the Chelsea line-up after missing the tour of the US with a goal before Sterling lifted the ball over Udinese goalkeeper Marco Silvestri following Jorginho’s pass.
Centre-back Kalidou Koulibaly also made his first Chelsea start since signing from Napoli.
Chelsea open the 2022-23 Premier League season away to Everton on Saturday, 6 August.
Elsewhere, Chris Wood’s first-half penalty was enough for Newcastle to beat Serie A side Atalanta at St James’ Park.
Newcastle host Athletic Bilbao on Saturday before entertaining newly promoted Nottingham Forest on 6 August.