In a game of few clear-cut chances, Edouard Mendy marked his return from injury with an excellent save to claw away Nemanja Gudelj’s deflected header after it had flicked off Kurt Zouma.
Sevilla, last season’s Europa League winners, showed off their experience on the European stage.
Former Liverpool forward Suso headed wide before Lucas Ocampos forced another save from Mendy after Zouma’s poor clearance.
Chelsea improved after the break, French defender Zouma and Ben Chilwell both heading chances straight at goalkeeper Yassine Bounou.
Sevilla went close to taking the lead in spectacular fashion through substitute Joan Jordan’s dipping volley from a corner.
With Group E rivals Rennes held 1-1 in France, Chelsea head to Russia next Wednesday to face Krasnador with all four teams on one point.