Chelsea opened up a 2-0 lead over Servette as they registered the first win of the Enzo Maresca era.
Christopher Nkunku won and scored a penalty early in the second half before Noni Madueke was teed up by fellow sub Enzo Fernandez to score 15 minutes from time.
Despite being a fairly lacklustre display from the Blues, it was enough to create a sizeable advantage for next week’s trip to Switzerland and the second leg of this UEFA Conference League play-off tie.
Enzo Maresca made nine changes to the team that lost to Manchester City on Sunday with only Moises Caicedo, who captained the team for the first time, and Nkunku remaining.
That meant full debuts for six summer signings, amongst them striker Marc Guiu who was inches from opening the scoring in the second minute, rounding the goalkeeper from fellow full debutant Dewsbury-Hall's through pass but failing to reach the ball before it squirmed from his reach behind the goal.
Servette carried their own threat and broke through Chelsea's lines when Kutesa played a one-two inside the box with Keigo Tsunemoto before streaking past Axel Disasi and striking a low effort that was deflected away by goalkeeper Filip Jorgensen.
Chelsea were relying heavily on their two wide forwards, Mykhailo Mudryk and Pedro Neto, but though both were frequently on the ball, neither player provided the delivery or penetration necessary to find a way in behind Servette.
There was more success when Mudryk tried to cut inside. Guiu held the ball up well for him midway through the first half giving the Ukrainian room to shoot, but he dragged his shot tamely wide of the post.
Nkunku sought a more central route through, intercepting a loose pass and charging through the middle to feed Mudryk, who slipped it wide for Neto to come inside and shoot left footed. His effort lacked bite and landed cleanly in the arms of Jeremy Frick, encapsulating Chelsea's first-half labours.
One and a half matches into Maresca's tenure, the team left the pitch to a smattering of jeers from home fans.
Chelsea's play had been breaking down in wide positions, but in the second minute after the interval Dewsbury-Hall sought to play directly down the middle, finding the run of Nkunku who reached the ball before Frick and, though heading away from goal, was brought down. From the resulting penalty, he fired calmly into the corner for 1-0.
Guiu made a horrendous mess of an open goal, before Maresca sent on Cole Palmer in search of a creative glint.
Instead it was two other second-half substitutes who provided the goal, Enzo Fernandez launching the ball up the right wing for Madueke to streak onto it and lash the ball in at the near post to settle nerves.
Jorgensen saved well to his right from Jeremy Guillemenot after Chelsea gave the ball away in defence, before Tiemoko Ouattara cracked the bar as Chelsea survived gratefully with their two-goal lead in tact.
