Zenit scored the first goal of the group stage through Sardar Azmoun but Lyon hit back six minutes into the second half with a penalty earned and scored by Depay.
Both teams pushed for victory in Tuesday's Group G game but were unable to find a late breakthrough.
Lyon started on top with Moussa Dembele curling a shot narrowly over the crossbar, although Branislav Ivanovic had wasted a free header at the other end.
Marcelo then nodded wide from a Depay corner as Lyon continued to press, but Zenit opened the scoring against the run of play in the 41st minute.
A clever one-two with Artem Dzyuba on the edge of Lyon's box sent Azmoun through and he poked his finish past onrushing goalkeeper Anthony Lopes.
Lyon pulled level early in the second half, though, Depay coolly converting a penalty he won himself by drawing a foul from Magomed Ozdoev in the area.
The equaliser boosted Lyon and Jeff Reine-Adelaide should have put them in front after Zenit were carved open, the former Arsenal youngster instead firing wide from the edge of the box.
6 - Lyon have drawn each of their last six UEFA Champions League home games; a record for a team in the competition. Generous. pic.twitter.com/LVBxrBU2ns— OptaJean (@OptaJean) September 17, 2019
That opportunity proved the clearest chance to score a winner for either side, with the spoils shared after Depay failed to make the most of being played in by Reine-Adelaide.
What does it mean? Group G looks wide open
The result will have pleased all four teams who landed in this group, which looks the most unpredictable of the eight sections. Each club, including Benfica and RB Leipzig, will fancy their chances of progressing with the top two spots completely up for grabs.
Depay leads Lyon recovery
Lyon were on top in the first half without creating a great deal, but after the break Depay stepped up. The Netherlands forward can be inconsistent but won the penalty with a moment of magic that was far too good for Ozdoev to deal with.
Of Lyon's last five Champions League goals, Depay has been directly involved in four.
Zhirkov anonymous for Zenit
One of the most experienced players in the competition, 36-year-old Yuri Zhirkov did not offer enough creativity on the wing for the Russian champions. It was no surprise to see coach Sergei Semak replace him with Daler Kuzyaev midway through the second period.
Zenit are at home to Rubin Kazan in the Russian Premier League on Saturday, the day before Lyon host Ligue 1 champions Paris Saint-Germain. Matchweek two of the Champions League, played early next month, sees Lyon go to Leipzig, while Zenit host Benfica.