From 1963-66, Knap served as the head football coach at Utah State, where he compiled a 25-14-1 (.637) record. In 1968, he succeeded Lyle Smith at Boise State, then still known as Boise College. It was the school's first year in Division II (then the "college division"); it had previously competed (and dominated) in the junior college ranks. Knap led the Broncos to a 71-19 (.788) record in 8 years, including three 10-win seasons.
His success in Boise led him to Las Vegas in 1976, where he coached UNLV for six seasons and compiled a 47-20-2 record (.695) from 1976-81. UNLV made the Division II playoffs in his first season and moved up to Division I-A in 1978, his third season at the school. While Knap was head coach, the Rebels played as an independent; UNLV joined the PCAA in 1982. He was inducted into UNLV's hall of fame in 1989.