Born in Toronto, Ontario, Neilson's coaching career began when he became head coach of the Ontario Hockey League's Peterborough Petes in 1966. He then moved on to the National Hockey League, where he was head coach of the Toronto Maple Leafs from 1977 to 1979, the Buffalo Sabres from 1980 to 1981, the Vancouver Canucks from 1981 to 1984, the Los Angeles Kings in 1984, the New York Rangers from 1989 to 1993, the Florida Panthers from 1993 to 1995, the Philadelphia Flyers from 1997 to 1998 and 1999 to 2000, and the Ottawa Senators for two games in April 2002. He was assistant coach of the Senators at the time, but was appointed head coach so he could become the ninth man to coach 1000 games. His overall regular season record was 460 wins, 381 losses, and 159 ties.
Neilson dedicated his entire life to coaching and to hockey and affected the careers of thousands. He had no family and would stay up late into the night watching video and analysing games.
Among his most well-known innovations was the use of videotape to analyze other teams, leading to the nickname "Captain Video." He was also the first to use microphone headsets to communicate with his assistant coaches.
Neilson was well known for closely reading the rule book looking for loopholes. During one particular game in the OHL his team was up one goal, but was down two men in a five on three situation for the last minute of the game. Realizing that more penalties could not be called under the existing rules, Neilson put too many men on the ice every ten seconds. The referees stopped the play and a faceoff was held relieving pressure on the defence. After this display the rule was changed so that a call for too many men on the ice in a 5 on 3 situation now leads to a penalty shot.
Neilson also discovered that if he put a defenceman in net instead of a goalie during a penalty shot, the defenceman could rush the attacker and greatly reduce the chances of a goal. Today the rule states that a team must use a goalie in net for a penalty shot.
Neilson also broke the rules, in a sense, when he didn't like what was going on on the ice. As the Canucks coach during a 1982 playoff game against the Chicago Blackhawks, he felt his team was unfairly penalized on several occasions during the third period. He took a white trainer's towel and held it on a hockey stick, as if to wave a white flag. Three other Canucks players did the same thing, and all were ejected from the game. (Neilson inadvertently started an NHL tradition by doing so - Canucks fans waved white towels by the thousands at the next game, and other teams have copied the tradition.)
He was inducted into the Hockey Hall of Fame as a builder in November 2002.
In 1999, Neilson was diagnosed with bone cancer, which spread to become skin cancer in 2001. He died at age 69 on June 21, 2003.