Romelu Lukaku’s goal was enough to give holders Chelsea a victory in their opening Champions League group match.
Lukaku struck midway through the second half – his fourth goal in as many matches since returning to Stamford Bridge.
The Belgian striker headed Cesar Azpilicueta’s right-wing cross into the far corner of the net.
Russian side Zenit St Petersburg defended well to frustrate the Blues – and Artem Dzyuba missed a great chance to equalise for them when he contrived to poke the ball wide from close range.
Earlier, Chelsea defender Antonio Rudiger almost opened the scoring in spectacular fashion when he stormed forward from inside his own half, dodged two challenges and fired narrowly wide.
Chelsea: Mendy, James, Azpilicueta (Silva 83), Christensen, Rudiger, Alonso (Chilwell 83), Kovacic, Jorginho, Mount (Loftus-Cheek 90), Ziyech (Havertz 64), Lukaku.