There was relief around Stamford Bridge at the full-time whistle as Chelsea were made to work hard for their win and survived some awkward moments.
Servette registered 22 attempts to the hosts' 14, with substitute Tiemoko Ouattara hitting the bar with a deflected effort in the 86th minute.
However, Chelsea eked out a victory to help put the disappointing opening defeat by Manchester City behind them and get Maresca's reign up and running.
"I was a bit worried because in the last 10 minutes we played a little bit with fire," said Maresca. "It was good that we didn't concede but we can learn."
The Blues boss made nine changes from the team which started at the weekend, yet finished it with five substitutes on the pitch including Cole Palmer, Enzo Fernandez and Malo Gusto.
Goalkeeper Filip Jorgensen and defender Tosin Adarabioyo made their debuts, while there were also first starts for Kiernan Dewsbury-Hall, Guiu, Renato Veiga and Pedro Neto.
Portugal forward Neto, a £54m buy from Wolves, produced a bright performance and at times showed an explosive change of pace before being replaced by Madueke.
There will be bigger tests to come for Chelsea, who were captained by Moises Caicedo - the other player, alongside Nkunku, who started Sunday's league defeat.
But after a chaotic summer which has seen another change of manager and their transfer policy come under heavy scrutiny, the Blues were at least able to celebrate a victory.