Leipzig scored two second-half goals to seal the deal while the Russian outfit scored a crucial away goal through Domenico Criscito on Thursday evening, keeping the visitors' hopes alive for the second leg, reports Xinhua news agency.
Leipzig grabbed the reins from the start but remained wasteful in front of goal in the first half as Emil Forsberg rattled the woodwork following a free kick before Timo Werner pulled wide from promising range before the break.
Zenit focused on their defensive work and tried to keep the hosts at a distance. However, the visitors posed no threat in the first 45 minutes.
After the restart, Leipzig started where they left off and pressed forward as Werner's back-heel at the edge of the box allowed Bruma to slot home to open the scoring.
With the narrow lead, Leipzig gained momentum and piled on the pressure. The hosts' efforts paid off in the 77th minute when Naby Keita's build up play and pass allowed Werner to slot home from an acute angle.
It seemed Ralph Hasenhuettl's men would take a 2-0 victory but Zenit reduced the deficit out of the blue through Domenico Criscito, who curled a free kick over the wall into the top left corner to make it 2-1.
Zenit's away goal might be a costly one, as the visitors keep the tie open for the second leg in Saint Petersburg next week.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)