Bellows played junior hockey in the Ontario Hockey League with the Kitchener Rangers. During this time, he was featured in Sports Illustrated, which described him as the hottest prospect since Wayne Gretzky.
Bellows was drafted second overall by the Minnesota North Stars, who had acquired the draft pick in a trade with Detroit with the purpose of having a shot at Bellows. North Stars GM Lou Nanne sent Don Murdoch, Greg Smith, and a first round pick (Murray Craven) to the Wings in exchange for what later turned out to be the second overall draft pick. Bellows was often compared to Gretzky, which led to a tough rookie season. The pressure of such comparisons caused criticisms when he did not live up to them. Bellows improved greatly in the second half of the season and finished with 35 goals. In the playoffs that year, Bellows scored 9 points (5 goals, 4 assists) in 9 games.
Bellows played 10 seasons with the North Stars and was popular in Minnesota for his charity work, as well as his goal-scoring. He had a North Star record 342 goals in 753 games, peaking with 55 goals in 1989–90. In 1990–91, Bellows scored 29 points in the post-season to become the North Stars career playoff point leader, and took the North Stars to the Stanley Cup finals where they fell to the Pittsburgh Penguins.
When team captain Craig Hartsburg was injured partway through the 1983–84 season, Bellows was named interim captain for the remainder of the season. At 19 years and 4 months, Bellows became captain at an earlier age than Connor McDavid, Gabriel Landeskog and Sidney Crosby. However, because he was an interim captain, McDavid is still considered the youngest captain in history.
On August 31, 1992, Bellows was traded to the Montreal Canadiens for Russ Courtnall. The trade angered Bellows at first, but he relished the chance to play for the Canadiens. Bellows remarked "I hope to score more than last year. I want to come in and prove I can still play to the levels expected. I was shocked [about the trade] but I'm excited about the new change. My idol was Ken Dryden. It's every kid's dream to play for the Canadiens." In the 1992-93 NHL season his 88 points were the second highest season total of his career, and his 15 playoff points helped the Canadiens win the Stanley Cup in 1993.
As his career was winding down, Bellows played for the Tampa Bay Lightning, Mighty Ducks of Anaheim and the Washington Capitals. In the 1997–98 NHL season the Capitals made it to the Stanley Cup finals, but lost to the Detroit Red Wings. En route to the Eastern Conference championship, Bellows scored the series-clinching overtime goal in the first round in Game 6 against the Boston Bruins. The 1998–99 season was his last. On January 2, 1999, Bellows scored his 1000th career regular season point, becoming the 54th NHL player to reach that plateau.
Bellows was named to the 1990 Second All-Star team, and played in three NHL All-Star Games (1984, 1988 and 1992). He retired with 485 goals, 537 assists and 1,022 points. He was named the top forward at the 1989 World Ice Hockey Championships, as Canada won the silver medal.
Brian Bellows lives in Edina, Minnesota, and works in Minneapolis as a broker at investment bank Piper Jaffray.
Bellows' son Kieffer Bellows plays hockey for the Portland Winterhawks of the Western Hockey League, and in 2016 was drafted in the first round, 19th overall, by the New York Islanders.Member of one Stanley Cup winning team: 1993 with the Montreal Canadiens
Selected to three NHL All-Star Games: 1984, 1988 and 1992
Selected to the 1990 NHL Second All-Star Team