He played junior hockey with the Hamilton Tiger Cubs of the Ontario Hockey Association. After scoring 90 points in 52 games a 20 year-old, he signed his first professional contract with Detroit and was assigned by the Red Wings to the Edmonton Flyers of the Western Hockey League.

Oliver scored 20 goals in his rookie season as a Red Wing in 1959-60, but the Wings were loaded at the centre ice position, so they traded him to Boston during the following season. He centred the Bruins B.O.W. line with Johnny Bucyk and Tommy Williams as his wingers.He had a career high 68 points in 1964, despite knee surgery the previous campaign.

Oliver, a fine stickhandler and playmaker, played with the Bruins for seven years, before being dealt to Toronto in 1967. For three years he centred a line with Bob Pulford and Ron Ellis. He was then traded to Minnesota in 1970.

Oliver played five seasons with the North Stars and notched a career best 27 goals in the 1971-72 season. But after a bitter contract dispute with the Stars, he retired.

Oliver had an outstanding 18 year career in the NHL. He played 1127 regular season games scoring 274 goals with 454 assists for 728 points. He played in five All-Star games.

After retiring, he was hired by former teammate Lou Nanne, as Minnesota’s assistant coach. He worked with the club until the 1985-86 NHL season, with 37 games as head coach. He was as a scout with the Vancouver Canucks and later took over as the club’s director of pro scouting.

On November 23, 2014 Murray Oliver died of a heart attack at the age of 77.