The highly skilled Russian winger was drafted in the 9th round, 263th overall by the Columbus Blue Jackets in the 2002 NHL Entry Draft. In 2005–2006 Russian Super League regular season Mozyakin had a tight scoring race with Aleksey Morozov and Evgeni Malkin for the top scorer of the league. Mozyakin finished the season leading the league in points (52). In 2007-08 regular season, which would be its final in existence before being absorbed into the Kontinental Hockey League, Mozyakin had another tight scoring race with Morozov and finished the season with only one point ahead of Morozov, leading the league in goals (37) and points (64). In 2009-10, Mozyakin finished top scorer of the Kontinental Hockey League with 66 points (27 goals and 39 assists).
Mozyakin has also been a regular member of the Russian national team, taking part of all the 12 EHT games in the 2007-2008 season, in which he scored 4 goals and 3 assists for 7 points.