Ellett had hockey in his genes; he was born in Cleveland because his father, Bob Ellett, was playing for the Barons of the American Hockey League at the time.

The Winnipeg Jets selected the 6-foot-2 defenseman in the fourth round (No. 75) of the 1982 NHL Draft. He opted to play college hockey instead of major juniors and spent two seasons at Bowling Green. He turned pro after helping the Falcons win the NCAA championship in 1984.

Ellett was an instant success in the NHL. He scored at least 11 goals for Winnipeg in each of his first six seasons, including an NHL career-best 22 in 1989-90. In the 1990 Stanley Cup Playoffs, his double-overtime goal in the Smythe Division Semifinals against the Edmonton Oilers gave the Jets a 3-1 lead in the best-of-7 series; although the Oilers rallied to win the series, his goal has long been regarded as one of the high moments in Jets history.

The Jets traded Ellett to the Toronto Maple Leafs on Nov. 10, 1990, and though he reached double figures in goals (18) for the final time in his NHL career in 1991-92, his all-around game improved. Ellett played a key role in helping the Maple Leafs reach the Western Conference Final in 1993 and 1994, contributing 30 points (seven goals, 23 assists) in 39 playoff games during those two years and setting team playoff records for assists (15) and points (18) by a defenseman in 1994.

Toronto traded Ellett to the New Jersey Devils on Feb. 25, 1997. He finished the 1997-98 with New Jersey, played two seasons with the Boston Bruins and one with the St. Louis Blues before retiring on Sept. 8, 2000. Ellett finished his NHL career with 568 points (153 goals, 415 assists) in 1,129 games, as well as 57 points (11 goals, 46 assists) in 116 Stanley Cup Playoff games.