Barulin began his career with Gazovik Tyumen in 2001. He had a brief spell with SKA Saint Petersburg before returning to Gazovik. He went on to have spells at Spartak Moscow and Khimik Moscow Oblast before joining CSKA Moscow for the inaugural KHL season in 2008. On 29 July 2010, after two years with CSKA Barulin returned to Atlant signing as a free agent on a two-year contract. In 2012, he signed a three-year contract with Ak Bars Kazan.
After one season with Avangard Omsk in 2014–15, Barulin left as a free agent to sign an initial one-year deal with HC Sochi of the KHL on 28 May 2015.[1]
Barulin remained as a standout starting goaltender in Sochi for four seasons. Following the 2018–19 season, Barulin left as a free agent to sign a one-year contract with Neftekhimik Nizhnekamsk on 2 May 2019.[2]
During his second year with Neftekhimik in the midst of the 2020–21 season, with the club well out of playoff contention and having collected just 2 wins through 21 games, Barulin left the KHL and signed for the remainder of the season with Czech top flight club, HC Dyanmo Pardubice of the ELH, on 21 January 2021.[3]