Heinze was drafted by the Bruins in 1988. He would move on to play three years at Boston College where he was a an all star and member of the famed HEM line with David Emma and Marty McInnis. Heinze left school early to play for the United States National Team and the 1992 U.S. Olympic team.
Following the Olympics Heinze jumped directly to the NHL, but for all his amateur promise he could never achieve extended periods of offensive success in the NHL. He carved out a traditional Bruins winger role of grinder. He also excelled as a penalty killer due to his great first step quickness. He played an intelligent third line game and was able to use decent playmaking and a quick snapshot to consistently challenge the 20 goal plateau. His best year came in 1997--98 when he notched 26 goals and 46 points. That season was particularly rewarding for him as he was limited just 30 games the year before because of serious knee and abdominal injuries.
The Columbus Blue Jackets selected him in the June 2000 Expansion Draft, and the Massachusetts native left home for the first time, heading West to Ohio for the new team's inaugural season. Heinze, who for the first time began wearing the obvious jersey number of 57, put in admirable effort, scoring 22 goals and 42 points in 65 games, but was traded to the Buffalo Sabres in a typical salary dump/youth movement trade deadline acquisition. The Sabres in the meantime were hoping he could experience, speed and grit to their playoff run. He added all of that plus 7 points in 13 playoff contests.
Heinze's stay in the Queen City was short as he signed with the Los Angeles Kings as a free agent. He would enjoy a year and a half in the Californian sunshine before being forced out of the game with post concussion syndrome. Heinze was viciously hit in the head with Brad May's stick. The incident landed May a 20 game suspension. Ironically Heinze earlier had testified at Marty McSorley's assault trial saying sticks to the head were part of the game.