Born in Sochi, Soviet Union, Zebelyan played different sports as a child, including tennis, before focusing more on football.

[2] Zebelyan started his career with Zhemchuzhina Sochi, where he made sixty-two appearances and scored nine goals.

[2] His first stint for Zhemchuzhina Sochi was only a few years after the club's only spell in the Russian Premier League.

[5] Before the 2011 season, Zebelyan signed for Dinamo Minsk, where he failed to completely establish himself as a starting player.

[12][13] He scored his first goal for Dinamo Minsk during a 1–0 win over Dnepr, the club's first win in four matches and the first goal his team scored after a goalless streak of 403 minutes, and temporarily eased the pressure on then Dinamo Minsk manager Oleg Vasilenko.

[5] In 2011, Zebelyan signed for Tobol Kostanay, debuting in the Champions League against Slovan Bratislava, but suffered an injury which caused him to get treatment in Armenia.