Zenit went ahead in Greece in the 39th minute, striker Pavel Pogrebnyak scoring on his 24th birthday. Larissa, which is, coincidentally, a popular Russian girl's name, hit back in the second-half, scoring twice, in the 58th and 63rd minutes to take a 2-1 lead.
However, Zenit, who will claim the Russian championship for the first time ever if they win on Sunday in the Premier League, leveled through Ziranov in the 70th minute, before their Turkish striker, Tekke, scored the winner eight minutes later.
Zenit's first 2007/08 UEFA Cup match on October 25 ended in a 1-1 draw with AZ Alkmaar of the Netherlands.
Spartak Moscow, currently in second place in the Russian Premier League. went ahead in Moscow in their Group E tie after Roman Pavlyuchenko, two-goal hero of Russia's recent 2-1 victory over England, converted a penalty in the 63rd minute. Spartak's Brazilian defender Mozart hit home another penalty in the 77th minute, before Bayer gave Spartak a fright with an injury time goal through Freier.
The match was Spartak's first in the 2007/08 group stage.
In the UEFA Cup group stages, each team plays two matches at home and two away, with the top three going through to the knockout rounds, where they will be joined by the eight teams finishing in third place in their Champions League groups.
Lokomotiv Moscow were also due to play later on Thursday evening in the UEFA Cup against Scottish club Aberdeen.