Peeters was born in a family of Dutch immigrants in Edmonton, Alberta. At a young age, he valued swimming more than hockey. It was not until he was 18 that Peeters was committed to junior hockey. In 1975, Peeters joined a struggling Medicine Hat Tigers team. He would stay with the Tigers for two years before being drafted. Peeters was drafted 135th overall by the Philadelphia Flyers in the 1977 NHL amateur draft after showing scouts that he had what it took to play at an NHL level. He played for two years in the AHL winning the Harry "Hap" Holmes Memorial Award for best GAA in the league and he was also selected to the First All-Star Team.
Playing career
Philadelphia Flyers
Peeters was called up by the Flyers in 1980 sharing the net with Phil Myre. Peeters started with a 22–0–5 record before losing his first game of the season on February 19. The Flyers went a NHL record 35 straight games without a loss that season. Peeters finished the season with a 29–5–5 record with a 2.73 GAA. He led the Flyers all the way to the Stanley Cup Finals before losing to the New York Islanders on an overtime goal by Bob Nystrom. For his effort, Peeters was selected to play in the NHL All-Star Game. The following season, expectations were high for Peeters but he did not meet them. Over the next two years his GAA rose and his playoff success diminished. In 1982, Peeters was traded to the Boston Bruins for defencemanBrad McCrimmon.
Boston Bruins
Peeters joined the Boston Bruins for the 1982–83 season. Peeters had perhaps his best year as he played in 62 games and posting a 40–11–9 record with 8 shutouts and a decade-best 2.36 GAA. At one point, Peeters went 31 games without a loss. He won the Vezina Trophy for his spectacular play and was selected First All-Star Team goalie. He also played in the All-Star Game in his first season with Boston. Surprisingly, Peeters finished 2nd in voting for the Hart Memorial Trophy to Wayne Gretzky. Next season, expectations were high again for Peeters and, like in Philadelphia, he did not meet them. He played for two more years with the Bruins with his GAA inflating and the losses piling up.
Peeters was invited to Team Canada for the 1984Canada Cup. Despite having a sprained ankle, Peeters was able to play in four tournament games including both best-of-three final games against Sweden and the memorable overtime win against the Soviets in the semifinal.
Washington Capitals
After the Canada Cup experience, Peeters had trouble readjusting his game to the NHL level. After a slow start in the 1985–86 season, Peeters was traded to the Washington Capitals in exchange for goaltender Pat Riggin. Peeters provided the Caps with solid goaltending for the next five seasons. But in the playoffs, Peeters did not find much success again.
Return to Philadelphia
Peeters returned to Philadelphia in 1990 by way of free agency. He remained there for the last two seasons of his career sharing the net with Ron Hextall and Ken Wregget. Peeters would hang up the pads in 1991.