Egan coached the Rockets from 1972 to 1976, leading the Houston version of the organisation to its first playoff appearance in 1975. Egan was one of the Rockets’ founding players when the team relocated to Houston before the 1971–1972 season. The Rockets’ 2-1 first-round victory against the New York Knicks was their first playoff series victory.
With the Detroit Pistons, New York Knicks, Baltimore Bullets, Los Angeles Lakers, and San Diego Rockets, Egan participated in 712 NBA games. He was a crucial rotation player for the 1968–1969 Lakers, who reached the Finals but fell to the Boston Celtics in Game 7. He averaged 7.8 points, 1.8 rebounds, and 3.0 assists per game. Alongside announcer Bill Worrell, Egan was a fairly well-known on-air broadcaster.