FCモスクワ
Zhevnov started his career at third division. In 2000, he was signed by BATE Borisov. During UEFA Cup 2001/02 qualification match against FC Dinamo Tbilisi Zhevnov scored a goal from his own half. In 2005, was signed by FC Moscow. On 23 February 2010 Zenit St. Petersburg signed the Belarus international goalkeeper from FC Moscow on a four-year deal.