Prust played three seasons of major junior hockey with his home town London Knights of the Ontario Hockey League (OHL). During his junior career, he won an OHL and Memorial Cup Championship. A Thorndale, Ontario, native, Prust was a walk-on during the Knights' open tryouts, having been bypassed in the OHL Priority Draft.
Prust was drafted by the Calgary Flames in third round, 70th overall, at the 2004 NHL Entry Draft, where he was sent back down to London to play his final OHL season. After spending the following season with the Omaha Ak-Sar-Ben Knights, Prust made his NHL debut on November 1, 2006, against the Detroit Red Wings.
Prust suffered an injury during the 2008–09 season when he broke his jaw after being elbowed by Cam Janssen of the St. Louis Blues. On March 4, 2009, Prust was traded, along with Matthew Lombardi and a 2009 first-round draft pick, to the Phoenix Coyotes in exchange for Olli Jokinen, and was then traded back to Calgary in exchange for Jim Vandermeer on June 27.
On February 1, 2010, Prust, along with Olli Jokinen, were traded to the New York Rangers in exchange for Aleš Kotalík and Chris Higgins. The Rangers re-signed Prust to a two-year, $1.6 million contract after the end of that season, 2009–10, on July 3.
In the 2010–11 season, Prust, a fourth-line utility player and occasional enforcer, was one of only seven NHL players to score at least ten goals as well as engage in at least ten fights. He was awarded the Steven McDonald Extra Effort Award at the end of the season, given to the Rangers player who "goes above and beyond the call of duty" as voted on by the fans.
Prust also played as the Rangers faced the Philadelphia Flyers in the 2012 NHL Winter Classic, which took place at Citizens Bank Park, Philadelphia, on January 2, 2012. Prust posted two assists in a 3–2 Rangers win. Prust proved to be a valuable member of the Rangers' penalty kill during his tenure there.
Prust became a free agent at the end of the season and signed a four-year, $10 million contract with the Montreal Canadiens on July 1, 2012, lasting until 2016.
After the start of the lock-out-shortened 2012–13 season, Prust scored his first goal as a Canadien against Martin Brodeur of the New Jersey Devils on January 27, 2013. Prust was awarded the Jacques-Beauchamp Trophy at the end of the regular season, an award voted on by the members of the media in Montreal to honour the team's unsung hero.
During the 2014 Eastern Conference Finals against his former team, the New York Rangers, Prust was suspended for two games following a hit on Rangers forward Derek Stepan during the first period of Game 3. Stepan suffered a broken jaw on the play and subsequently missed Game 4.
On July 1, 2015, he was traded to the Vancouver Canucks for Zack Kassian and Vancouver's 5th round draft pick in the 2016 NHL Entry Draft. Prust struggled with the Canucks, putting up the fewest points since his rookie 2008–09 season. On February 2, 2016, he was sent down to the Canucks' AHL affiliate the Utica Comets after clearing waivers. On March 10, he returned to his home in London, ON, and was taken off the roster due to an ankle injury. He became an unrestricted free agent on July 1, 2016.
Due to his ankle injury, teams were unwilling to give Prust a contract, with concerns raised over his foot speed and ankle itself. Going unsigned for the duration of the summer, he agreed to ink a Professional Try Out contract with the Toronto Maple Leafs on August 22, 2016. Prust's main reason for signing the try out was to fulfil his childhood dream of playing for the Maple Leafs, the team he grew up cheering for. He was released by the Maple Leafs on October 11, 2016, and embarked on his first overseas stint in late November 2016 after signing with the Nürnberg Ice Tigers of the German top-flight Deutsche Eishockey Liga (DEL). Prust is currently under a PTO (Professional Try Out) with the Los Angeles Kings, which are in the NHL's western division.
Prust grew up in London, Ontario, where he attended Regina Mundi Catholic College. While there, he excelled in multiple sports, and was recognized as the outstanding student athlete in 2000–01 school year. The number 8 he wore with the Canadiens is the same number he wore as a football player in high school. His favourite team growing up was the Toronto Maple Leafs, and his favourite player was Wendel Clark, after whom he has tried to model his game.
Prust has an uncle who was a Broadway actor. His interests other than hockey include golf and watching baseball.
Prust began dating Montrealer TV host Maripier Morin in 2010. On June 22, 2015, the couple got engaged and subsequently married in 2017.