As a youth, Rust played in the 2005 Quebec International Pee-Wee Hockey Tournament with the Detroit Honeyabaked minor ice hockey team. Rust played his collegiate career from 2010 to 2014 at the University of Notre Dame where he played a total of 161 games totaling 97 points. Rust finished his senior year as an alternate captain. Rust won a Gold Medal at the 2010 IIHF World U18 Championships for Team USA and the 2013 CCHA Tournament for Notre Dame. Rust was selected 80th overall in the third round of the 2010 NHL Entry Draft. Rust made his AHL debut during the 2013–14 AHL season for the Wilkes-Barre/Scranton Penguins. Rust made his NHL debut on December 13, 2014 for the Pittsburgh Penguins in a game against the Columbus Blue Jackets where the Penguins lost to the Blue Jackets in a shootout. He would score his first NHL goal two nights later against Evgeni Nabokov of the Tampa Bay Lightning, on December 15, 2014. Rust would enjoy a breakout year in 2016, due to injuries in the Penguins organization. After recording 8 points in 33 games in the 2015–16 season, Rust signed a 2-year extension with Pittsburgh, along with fellow players Scott Wilson, and Tom Kühnhackl. On May 26, 2016, at the NHL Eastern Conference Finals, Rust became the 8th rookie in history to get multiple goals in a game 7. On December 5, 2016, Rust first recorded his first career hat-trick in an 8–5 win over the Ottawa Senators. On April 20, 2017, Rust scored two pivotal goals, including the game-winner, in Game 5 of the Eastern Conference First Round meeting between the Penguins and the Blue Jackets. The Penguins ultimately won the game 5–2, and the series 4–1. He later went on to score the game winning goal in Game 7 of the Penguins next playoff series against the Washington Capitals. He has since been dubbed by Penguins fans as "Mr. Elimination" after scoring goals in game sevens. As a pending free agent after the 2017–18 season, Rust recorded career highs in assists and points. He helped propel the Penguins to the 2018 Stanley Cup playoffs, where they would lose in the second round to the Washington Capitals. On June 26, 2018, Rust signed a four-year contract to stay with the Penguins. The contract carries an annual average value of $3.5 million.
