Sterling, Koulibaly and Cucurella made their debuts as Chelsea ended a run of four consecutive defeats at Goodison Park despite a patchy performance.
Everton’s pre-season preparations were rocked this week by an injury that ruled England striker Dominic Calvert-Lewin out for the first six weeks of the season.
The Toffees suffered another injury blow early on when Ben Godfrey was stretchered off after coming off worse in a challenge with Kai Havertz.
Everton have been predicted to struggle again after just staving off relegation last season.
But they could easily have taken at least a point from a spirited display.
Chelsea goalkeeper Edouard Mendy made a fine save to prevent James Tarkowski heading Everton in front on his debut.
Sterling was also denied a debut goal by the offside flag after he swept home after Jordan Pickford spilled Mason Mount’s shot.
Everton’s good work before the break was undone in the eighth minute of added on time for the lengthy stoppage for Godfrey’s injury.
Ben Chilwell was bundled over inside the box by Abdoulaye Doucoure and, unlike in the Euro 2020 final, Jorginho sent Pickford the wrong way from the spot for the decisive goal.
Everton pushed valiantly in search of an equaliser after the break, but were blunt in attack without the presence of Calvert-Lewin or the departed Richarlison.
Mendy again rode to Chelsea’s rescue with important saves to turn Demarai Gray’s shot wide and block Doucoure’s powerful effort from point-blank range.
At the other end Sterling was frustrated again as his goalbound effort was deflected inches wide by Vitaliy Mykolenko
But one goal was enough for Chelsea to an five-year wait to win away to Everton.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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