The defender played the full 90 minutes as Zenit beat Lokomotiv Moscow on his debut in the Russian Super Cup, a trophy contested at the start of each season.
The Croatia centre-back, 31, joined the Russian club for £10.9m after playing in 10 Premier League games in 2019-20 for champions Liverpool.
Zenit are champions of Russia and start the 2020-21 Premier League season on 11 August against Rotor Volgograd.
Lovren was an unused substitute when Liverpool beat Tottenham in the 2018-19 Champions League final.