Zenit's control of the game slipped in the 41st minute when Viktor Fayzulin's crossfield pass was intercepted by Austria Vienna and Lodygin was forced to block Philipp Hosingers' low shot from 20 meters. A minute later, Tomas Simkovic had another chance for the visitors but fired straight into Lodygin's hands.
Despite being a man down in the second half, Zenit still created several chances after coach Luciano Spalletti sent on Roman Shirokov and Andrei Arshavin.
"We played a very good match," Spalletti said. "We dominated before we were one man down. When your opponent plays a closed football it's a very significant loss."
Unhappy with the red card decision, Spalletti added: "Unfortunately, such decisions usually spoil a game. We are now in a difficult situation, but I think it's in our hands to improve it."
Both teams have one point in the standings after each lost its opening match.
Porto was playing Atletico Madrid later in the group's other game.