Brunnström began playing professionally in Sweden's third highest hockey league with Jonstorps IF in 2005–06, scoring 44 points in 38 games. The following year, he joined Borås HC, helping their promotion to the second-tier Allsvenskan with a league-leading 73 points in 41 games. In 2007–08, Brunnström began garnering attention from the NHL while playing in the top-tier Elitserien with Färjestads BK. Undrafted by an NHL club, he was an unrestricted free agent in the NHL. Negotiations with Brunnström came to a head towards the end of the season, with the Detroit Red Wings, Montreal Canadiens, Toronto Maple Leafs and Vancouver Canucks widely considered to be the initial front-runners in landing him. Canucks general managerDave Nonis was reportedly close to signing Brunnström, but was fired before the deal could take place. After completing the season with 37 points in 54 games, Brunnström eventually signed with the Dallas Stars on May 8, 2008 to a two-year entry level contract. The deal was reportedly close to US$850,000 annually with bonus incentives that could increase his salary to US$2.5 million. After being a healthy scratch in his first two games with the Stars, Brunnström became the third player in NHL history to score a hat trick in his debut game on October 15, 2008, joining Alex Smart of the Montreal Canadiens and Réal Cloutier of the Quebec Nordiques, and later joined by Derek Stepan of the New York Rangers, Auston Matthews of the Toronto Maple Leafs and Ryan Poehling of the Montreal Canadiens. Brunnström was credited with the game-winning goal, helping the Stars to a 6-4 win over the Nashville Predators. He also scored a fourth goal in his debut game which was disallowed. Brunnström was placed on waivers by Dallas on October 15, 2010. He was assigned to the Stars' American Hockey League affiliate, the Texas Stars on October 18, after he cleared waivers. On January 13, 2011, Brunnström was traded to the Toronto Maple Leafs in exchange for Mikhail Stefanovich. On August 17, 2011, the Detroit Red Wings signed Brunnström to a pro tryout contract. Making the Red Wings' 2011–12 starting roster, on October 3, 2011, Detroit signed Brunnström to a one-year two-way contract which assured him $105,000 in AHL and $600,000 at the NHL level. He was, however, a healthy scratch for all but one of the Red Wings' first nine games, and on October 30, 2011 was placed on waivers. In 2012, he signed with Frölunda HC of the Swedish Hockey League, during the 2013–14 season, he transferred to fellow SHL side Leksands IF. After a short stint with the Malmö Redhawks and after sitting out the 2015–16 season, he re-signed with the Redhawks on June 1, 2016. After a years hiatus, Brunnström returned to the professional circuit for one last season in 2016–17, playing with Rungsted Seier Capital in the Danish Metal Ligaen. He scored 25 points in 37 games, before injury ended his season. He announced his retirement after helping Seier Capital claim the Danish championship.
