Career
Currently, he plays in the Russian Premier League for Football Club Zenit Saint St. Petersburg and its professional farm-club Football Club Zenit-2 Saint St. Petersburg. He made his debut in the Russian Premier League on 17 March 2013 for Football Club Zenit Saint St. Petersburg in a game against Football Club Mordovia Saransk. First choice Zenit goalkeeper Vyacheslav Malafeev was injured before the game.
Baburin entered the pitch after 10 minutes of play when Yuri Zhevnov who started the game picked up the muscle strain.