Before being selected by the Nashville Predators in the fourth round (No. 98) of the 2009 NHL Draft, Smith starred for Waterloo of the United States Hockey League. In 2008-09 he was second in the league in assists (48) and tied for second in points (76), was named to the USHL First All-Star Team and played in the USHL Prospects/All-Star Game.

After being drafted, Smith attended the University of Wisconsin, where he was named to the 2010 Western Collegiate Hockey Association All-Rookie Team after finishing ninth in NCAA freshman scoring with 33 points. He helped the Badgers advance to the 2010 NCAA championship game.

Smith was an alternate captain for the Badgers in 2010-11 and led them with 19 goals. One of two collegiate underclassmen to play for the United States at the 2011 IIHF World Championship, Smith was named one of the three best U.S. players after scoring a team-high three goals.

He joined the Predators for the 2011-12 season and had seven goals and 14 points in his first 15 NHL games. Among rookies, he finished tied for seventh in goals (14) and assists (22) and was second in power-play goals (six).

Smith made his Stanley Cup Playoff debut April 20, 2012, against the Detroit Red Wings and got his first NHL playoff point with an assist April 27, 2012, against the Phoenix Coyotes. He played for the United States at the 2012 IIHF World Championship and had two assists.

Smith tied for third on the Predators in power-play points (seven) and second in the NHL in shootout goals (five) in 2012-13. He won a bronze medal with the United States at the 2013 World Championship and was named one of the top three U.S. players after leading the team with 10 assists.

In 2013-14, Smith led the Predators with 24 goals and had 28 assists. He had his first four-point game (two goals, two assists) in the NHL on April 13, 2014, against the Minnesota Wild. That year Smith was named one of the United States' top three players at the World Championship for the third time in four years. He scored his first two playoff goals April 17, 2015, against the Chicago Blackhawks. He had an NHL career-high 25 goals in 2017-18 and had his fifth 20-goal season in 2018-19.

Smith came closest to winning the Stanley Cup in 2017, when the Predators reached the Stanley Cup Final before losing to the Pittsburgh Penguins in six games. He was limited to 10 games during the 2017 playoffs because of a high-ankle sprain, but played all six games of the Final, scoring a goal in Nashville's 5-1 win in Game 3 and getting an assist in a 4-1 victory in Game 4.

Smith got his 400th NHL point with an assist in the Boston Bruins' 4-3 overtime win against the Minnesota Wild on Oct. 22, 2022, and played his 800th NHL game Nov. 23, 2022, a 5-2 Bruins loss at the Florida Panthers. He signed a one-year, $1 million contract with the Dallas Stars on July 1, 2023.

Smith signed a one-year, $1 million contract with the Blackhawks on July 1, 2024. He was traded to the Detroit Red Wings on March 7, 2025, and played 19 games before announcing his retirement from the NHL at the age of 36 on Dec. 8. He had an NHL career-high 52 points (24 goals, 28 assists) in 2013-14 and scored an NHL career-high 25 goals in 79 games in 2017-18.