A defensive defenceman, known for his superb shot-blocking and bone-jarring bodychecks, Awrey played for the Niagara Falls Flyers of the OHA before being signed by the Bruins. Despite being an exceptionally fast skater, he rarely scored goals. He made his NHL debut in 1963–64 for the Bruins, his first of 16 seasons in the league. Awrey scored his first NHL goal on March 15, 1964 in Boston's 3-1 home win over Montreal.
Awrey was part of two Stanley Cup winning teams with the Bruins, in 1970 and 1972. He was also part of the Montreal Canadiens team that won the Stanley Cup in 1976, but did not play in any playoff games that season, and so does not have his name engraved on the cup for that year even though he qualified. Awrey was named to Team Canada for the Summit Series,[2] playing in two of the eight games.[1]