While playing in major junior hockey, Eagles played on perhaps one of the most talented teams of all-time - the Kitchener Rangers. When he joined the Rangers in 1980-81 as a 17-year-old, he became teammates with 17-year-old Al MacInnis and a pair of star 16-year-olds named Brian Bellows and Scott Stevens. The Rangers, despite being one of the youngest teams in the OHL, were the class of the league. They went on to represent the OHL at the 1981 Memorial Cup where they came up just short, losing in the finals to the defending champion Cornwall Royals. The Royals boasted the likes of future NHLers Dale Hawerchuk and Scott Arniel in their lineup.
NHL scouts certainly took notice of the Rangers. Bellows and Stevens were still too young to be drafted, so the focus was centered on MacInnis and Eagles, who wound up being selected by the Nordiques. In 1981-82, with their stars a year older and with some experience under their belts, it seemed Kitchener would be unstoppable on the way to the Memorial Cup. That proved to be true, despite the fact their star forward, Brian Bellows, missed a good part of the season with an injury. The Rangers went all the way winning the Memorial Cup. During the regular season Eagles contributed 66 points in just 62 games.
When Bellows, MacInnis and Stevens all graduated to the NHL, Eagles became the team leader with the Rangers in 1982-83, and although they remained a strong force in junior hockey, the team simply could not expect to reach the same level of success without those star players.
Eagles was called upon for two games with the Quebec Nordiques in 1983-84, but the balance of his rookie season was spent in the American Hockey League with the Fredericton Express. In 1985-86 he landed a roster spot with the Nords and played in 73 games, scoring eleven goals and 12 assists for 23 points as an NHL rookie. After two more years in Quebec, Eagles opted to sign as a free agent with the Chicago Blackhawks. After two years in Chicago, Eagles moved to the Winnipeg Jets where he would stay for over four years. Eagles was used primarily as a defensive specialist, with the aim being to shut down the opposing team's star players. He and Igor Ulanov were traded to the Washington Capitals for draft picks on April 7, 1995.
Eagles remained with Washington until the 1999-2000 season when his NHL career ended at the age of 37. He had played in 853 season games, with 74 goals, 122 assists and 196 points. He also had 34 playoff points in 44 games.