Gazzola played in the QMJHL for 3 seasons 2012–13 to 2013–14, was rewarded for his outstanding play when he was named to the 2013–14 QMJHL First All-Star Team.[1]
After his junior career, Randy went on to play CIS university hockey at the University of New BrunswickVarsity Reds. Randy made an immediate impact at UNB, being selected as the conference Rookie of the Year as well as being selected to the CIS All-Rookie team. He helped UNB to the 2015 University Cup final before losing to defending champion Alberta Golden Bears 6-3. Randy won a CIS national title (University Cup) with UNB the next season, March 2016, when they defeated their AUS rivals St. Francis Xavier X-Men 3-1 in the Championship final.
On January 13, 2021, Gazzola joined his second ECHL club, agreeing to a contract for the 2020–21 season with the Fort Wayne Komets.[2]