The hosts struggled to break down their opponents in the first half at Stamford Bridge before Christopher Nkunku put them in front with a 50th-minute penalty, just his fourth goal for the club.
Marc Guiu somehow contrived to miss an open goal a few minutes later, but Noni Madueke moved Chelsea closer to a group-stage place ahead of next week’s second leg by firing home from Enzo Fernandez’s pass.
Tiemoko Ouattara almost pulled one back for Swiss side Servette late on when his deflected strike hit the crossbar.
It was a welcome win for Chelsea after suffering a 2-0 loss in Maresca’s debut game against Manchester City at the weekend.
The Blues are making their return to European competition after finishing sixth in the Premier League last season under Mauricio Pochettino.
“We are learning how to manage the game,” said Maresca, who led Leicester to promotion to the Premier League last season.
“It was important to win the game with nine changes. There were many good things.”
But there was a scare for Chelsea, as key player Cole Palmer went down the dug-out holding the back of his leg at full-time after coming on as a second-half substitute.
“Cole felt something but he looks fine. Hopefully it is no problem and he can be available for Sunday’s game (against Wolves),” Maresca said.
Elsewhere, Greek club Panathinaikos suffered a 2-1 defeat at 10-man Lens in their first leg, with Wesley Said scoring what proved to be the winner for the Ligue 1 side.
Former Spain and Manchester United goalkeeper David de Gea endured a difficult debut as Fiorentina were held to a 3-3 home draw by Hungarians Puskas Akademia.
Irish club St Patrick’s kept their hopes of qualifying for the group stage of a European tournament for the first time alive, drawing 0-0 with Istanbul Basaksehir.
In the Europa League play-offs, Dutch giants Ajax thrashed Jagiellonia 4-1 in Poland, with English forward Chuba Akpom scoring a hat-trick.
Besiktas blew a 3-1 lead to draw 3-3 with Lugano in Switzerland, while Scottish outfit Hearts lost 1-0 at Viktoria Plzen.
© Agence France-Presse
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