Berenson played junior ice hockey with the Regina Pats, participating in two Memorial Cups in 1956 and 1958. In 1959, Berenson played for the World Champion Belleville McFarlands.
Berenson moved on to, and graduated from, Michigan's School of Business and played collegiately at the University of Michigan, winning All-American honors there with an NCAA-leading 43 goals in his final year.
He signed thereafter with the Montreal Canadiens, playing five years in their system and being on a Stanley Cup-winning squad in 1965 before being traded to the New York Rangers, where he played parts of two seasons without success.
Seven weeks into the 1967/1968 NHL season the St. Louis Blues acquired Red Berenson along with Barclay Plager from the New York Rangers. It was with the Blues where he became one of the new Western Division's first great stars, leading the Blues to three straight Stanley Cup finals and being named the division's best player by his peers in The Sporting News' annual poll each of those years.
His most notable scoring feat came on November 7, 1968, in a road game against the Philadelphia Flyers. Berenson scored six goals, including four over a nine-minute span. He became the first player to score a double hat trick on a road game. The six-goal total was one shy of the all-time NHL record (set by Joe Malone in 1920), and has been accomplished only once since.
Berenson was named team captain in 1970; however, as he was already 31 years old, the Blues felt his skills could only decline, and traded him in what was considered a shocking deal to the Detroit Red Wings, a multi-player trade receiving centre Garry Unger in return. He was an impact player for Detroit for four seasons, but was having a poor fifth season when he was dealt back to the Blues. The trade rejuvenated him, and he was an effective player for three and a half more seasons before he retired after the 1977–1978 campaign.
Berenson played in the legendary eight-game Summit Series for Team Canada against the Soviet Union in 1972, as well as in the “old-timers” rematch of the Canada Cup in 1987. He played in six NHL All-Star Games.
Altogether, in 17 NHL seasons, Berenson recorded 261 goals and 397 assists in 987 games.
Berenson retired from playing in 1978 and joined the Blues' coaching staff. He became the team's Head Coach midway through the 1979–80 season. A year later, he won the Jack Adams Award as the NHL's Coach of the Year. He returned to his Alma Mater as Head Coach in 1984 and remained in the position for 33 seasons. Berenson has led the Wolverines to 11 Frozen Four appearances, and NCAA championships in 1996 and 1998. In CCHA competition, his teams have won 11 regular-season and 9 tournament titles. In addition, Berenson's squads qualified for the NCAA Tournament for 22 consecutive seasons from 1991 to 2012. This is the longest streak ever in college hockey history. The Wolverines have also won 13 Great Lakes Invitational titles under Berenson.
On January 10, 2015, Berenson became the fourth coach in Division I men's hockey history reach 800 career wins.
Berenson was named the 2015–16 Big Ten Coach of the Year after leading the Wolverines to a 22–7–5 regular-season record, including a 12–5–3–2 record in Big Ten play.
On April 10, 2017, Berenson announced his retirement as head coach of the Michigan Wolverine men's ice hockey team following 33 years. He finished his career with an 848–426–92 record in 1,366 games, and helped lead Michigan to a record 36 NCAA tournament appearances.