Persson made his playing debut as an 18-year-old defenceman with Piteå IF. In 1973 he joined Brynäs. While with Brynäs, he received his first national championshipsilver medal and two national championship gold medals, in 1976 and 1977. It was during this time that the New York Islanders drafted him, so Persson decided to go overseas to play in the NHL. Persson's responsible, defensive style was endorsed highly by the Islanders head coach, Al Arbour, and Persson's career in the NHL started swiftly. Persson also showed an adept passing ability and an occasional scoring touch. This was no more apparent than during the Islanders first Stanley Cup playoffrun in Game 1 of the 1980 Finals against the Philadelphia Flyers. It was late in the third period, when Persson scored the game-tying goal to force a sudden-death overtime that the Islanders won. Outdoing his regular season output of four goals, Persson scored five goals in the 1980 playoffs, and had serious consideration to become the first Swede to capture the Conn Smythe Trophy, which is awarded for MVP of the Stanley Cup playoffs. Persson was part of the first NHL team to win a Stanley Cup with Europeans on its roster. The Islanders, with Persson as a regular on their backline, captured four consecutive Stanley Cups. He also set another record with the Islanders, playing more games than any other Swedish player in the NHL at that time. During nine seasons with the Islanders, including playoffs, Persson played in 724 games, scored 59 goals and had 367 assists. He sent the four diamond rings he received for the four Stanley Cup wins to his father, Gösta, in the northern city of Piteå, where he had begun his hockey career. During the late stages of the 1985–86 season, the Islanders management, starting to lose the commitment from its owner to its product, decided that it was no longer prudent to pay Persson's salary, so they traded him to the Winnipeg Jets for a player to be named later. Persson had become a part of the community on Long Island, his only U.S. residence, and was so distraught about the trade that he decided, almost immediately, not to report to Winnipeg, and instead retired from the NHL altogether. Instead, he returned to Sweden and joined Sweden's big-league Borås HC, and was later given an administrative position with the team. After that he was asked to become the national junior team's general manager. He was inducted into the Piteå Wall of Fame in 2006.