The departure of Kari Eloranta prior to the 1985–86 NHL season created an opening on the Flames' defense. Suter excelled in training camp and not only earned a spot on the team, he was quickly recognized by head coach Bob Johnson as the team's best overall defenseman. He scored his first two goals in his second NHL game, a 9–2 victory over the Los Angeles Kings, and by mid-season was among the NHL's rookie scoring leaders. He was one of two first-year players (along with Wendel Clark) to play in the 1986 All-Star Game, while his offensive production and ability to play in all situations made him a top contender for the Calder Memorial Trophy. Suter finished the season with 18 goals, and his 68 points tied Al MacInnis for the team lead for scoring among defensemen. He added ten points in ten playoff games, but was knocked out of the post-season in the Smythe Division Final against the Edmonton Oilers after suffering stretched knee ligaments following a hit by Mark Messier. Suter watched as the Flames reached, and ultimately lost, the 1986 Stanley Cup Finals to the Montreal Canadiens. Following the season, he was named to the All-Rookie Team on defense and was voted the winner of the Calder Trophy. Suter was the third American-born player to win the award, given to the NHL's top rookie.
The knee injury hampered Suter throughout much of the 1986–87 season; he attempted to play through it, but ultimately missed 12 games. Nonetheless, he still scored 49 points in 68 games played. Healthy for 1987–88, Suter had the finest season of his career. His 70 assists and 91 points were the highest single season totals he would record in his career. He played in his second All-Star Game, was named a Second Team All-Star and was a finalist for the James Norris Memorial Trophy as the NHL's top defenseman. Suter appeared in his third All-Star Game in 1988–89, but missed 16 games after undergoing an emergency appendectomy. He had 62 points in 63 games. As had happened in 1986, Suter was injured in the early stages of a deep post-season run by the Flames. He missed most of the 1989 Stanley Cup playoffs after suffering a broken jaw in Calgary's opening round series against the Vancouver Canucks. He watched as the team won the Stanley Cup in six games over Montreal.