During the 2011–12 season, Pastrňák led the Czech under-18 league in goals (41) and points (68). After being drafted by the Boston Bruins in the 25th pick overall in the 2014 NHL Entry Draft, Pastrňák signed a three-year, entry-level contract on 15 July 2014.
Pastrňák attended the Bruins' training camp for the 2014–15 season before being assigned to the Providence Bruins, the team's American Hockey League (AHL) affiliate, on 7 October 2014. He made his NHL debut with the Bruins on 24 November, logging 7:53 of ice time in a 3–2 overtime loss to the Pittsburgh Penguins. He scored the first two goals of his NHL career against Ray Emery on 10 January 2015, as the initial pair of goals resulting in a 3–1 Bruins' road win over the Philadelphia Flyers. On 29 March, Pastrňák became the youngest Bruins' player in history to score an overtime, game-winning goal in regular season play in Boston's 2–1 road win over the Carolina Hurricanes. At the end of the season, he was one of just two players selected in the 2014 NHL Entry Draft to play in more than 40 NHL games during the 2014–15 season, and along with fellow Bruins' rookie Ryan Spooner, led the team in offense during the last 20 games of the season.
Pastrňák has represented the Czech Republic's national teams at every level and has led his team in scoring numerous times. He won bronze at the 2013 Ivan Hlinka Memorial Tournament and in 2014 he won silver at the 2014 IIHF World U18 Championships. In 2016, he joined the Czech Republic national team for the first time at the 2016 IIHF World Championship where the team finished fifth. He also represented the Czech Republic at the 2016 World Cup of Hockey. Following the Bruins' defeat by the Tampa Bay Lightning in the Second Round of the 2018 playoffs, Pastrňák was invited to participate at the 2018 IIHF World Championship.