The 2011-12 season was a monumental one for Schwartz.

Playing his sophomore NCAA season alongside older brother Rylan, Schwartz finished as Colorado College's scoring leader with 41 points (15 goals) in 30 games. He also was captain of Canada at the 2012 World Junior Championship, where he had two goals and five points in six games and won a bronze medal.

After the college season, on March 12, 2012, Schwartz signed an entry-level contract with the St. Louis Blues, who had selected him in the first round (No. 14) of the 2010 NHL Draft. He played seven games for the Blues late in 2011-12, scoring a power-play goal in his NHL debut March 17, 2012, against goaltender Dwayne Roloson and the Tampa Bay Lightning, and scoring again in his second League game, March 21 against the Anaheim Ducks.

After splitting the 2012-13 regular season between the Blues and Peoria of the American Hockey League, Schwartz made his Stanley Cup Playoff debut April 30, 2013, against the Los Angeles Kings. He had back-to-back 20-goal seasons with the Blues in 2013-14 (25) and 2014-15 (28).

An ankle injury kept Schwartz out for 49 games in 2015-16, but he returned to score 18 points in his last 26 regular-season games. In the playoffs he had points in six consecutive games and a three-game goal streak, finishing with four goals and 14 points in 20 games and helping St. Louis reach the Western Conference Final.

An explosive skater, Schwartz was a dominant force with Notre Dame of the Saskatchewan Junior Hockey League, where he had 34 goals and 76 points in 46 games in 2008-09. He played for Canada at the 2009 Ivan Hlinka Memorial Cup, getting a goal and an assist in a 9-2 win against Russia in the gold-medal game.

Schwartz led the United States Hockey League with 83 points (33 goals) in 2009-10 with Tri-City and was named the league's Offensive Player of the Year. He had a team-high 47 points in 30 games for Colorado College in 2010-11, leading freshmen nationally with 1.57 points per game, and won a silver medal with Canada at the 2011 World Junior Championship, though his tournament was cut short because of a broken ankle.