A slick-skating, puck-moving defenseman, Schultz was drafted by the Anaheim Ducks in the second round (No. 43) of the 2008 NHL Draft but had already committed to the University of Wisconsin.

Schultz made his mark with the Badgers, earning Western Collegiate Hockey Association All-Rookie honors as a freshman with 22 points in 43 games in 2010. In his sophomore and junior seasons Schultz was named WCHA Defensive Player of the Year. In his final two seasons at Wisconsin, Schultz combined to score 34 goals and 91 points in 78 games.

Following his junior season in 2012-2013, Schultz announced he was turning pro but was unable to come to terms on a contract with Anaheim and became a free agent. He eventually signed with the Edmonton Oilers.

Schultz started the 2012-13 season with Oklahoma City of the American Hockey League, where the 6-foot-2, 193-pound defenseman showed his strong offensive game and instincts with 18 goals and 48 points in 34 games to start the season. Even though he was called up to Edmonton when the NHL resumed play in January following a labor stoppage, Schultz won the Eddie Shore Award as the AHL's top defenseman for 2012-13.

That season, he also was named to the NHL All-Rookie Team after scoring eight goals and 27 points in 48 games with Edmonton. During his fourth season with the Oilers, Schultz was traded to the Pittsburgh Penguins on Feb. 27, 2016.

Joining the Penguins for the stretch run, Schultz had eight points in 18 regular-season games. He would play 15 playoff games, including all six in the 2016 Stanley Cup Final, to help Pittsburgh win the championship.

Schultz scored 51 points (12 goals, 39 assists) in 78 games in 2016-17 and had 13 points (four goals, nine assists) in 21 playoff games to help the Penguins win the Stanley Cup for a second straight season.