Victor Moses contributed to the only goal in the match as he produced a fine display to setup Islam Slimani to score the only goal for Fenerbache in the 21st minute.
Fenerbache however continued to press forward but the visitors also gave an account of themselves.
Since joining Fenerbache on loan from Chelsea, the midfielder has been involved in most goals of the club.
Victor moses now have two assist and a goal for Fenerbache in four matches.
Zenith failed to put the match back on level terms as Mak missed a penalty in the 44th.
Fenerbache now take a goal advantage into the second leg in Russia next week thursday.