He began his career by FC Gomel 1999, joined 2004 to Russian club Sokol Saratov, plays here in the reserve and turned to end of the season in January 2005 back to Belarus and signed a contract by BATE Borisov. Bliznyuk was generally a starter for BATE Borisov during their successful 2008–09 Champions League campaign. He netted twice against Icelandic side Valur on 15 July 2008 and also scored an important goal in the 2–2 home draw with Belgian club Anderlecht on 6 August 2008. On 27 August 2008, he was sent off on the stroke of half time in the return leg against Levski Sofia, but the match ended in a 1–1 draw and BATE qualified to the group stage of the Champions League for the first time in their history. Bliznyuk participated in four of BATE's matches in the group stage. He left BATE on 13 January 2009 and signed a six-month contract with FSV Frankfurt.