Arizona is one of four unbeaten teams remaining in major college basketball and the Wildcats survived thanks to a replay decision at the end of regulation.
After trailing by 16 points with 12:45 to play in the second half, the Wildcats rallied to tie it at 80-80 on two free throws by Lyons with 9 seconds remaining.
Colorado's Sabatino Chen then put up what appeared to be the game-winning shot, a 3-point attempt that banked in as the buzzer was sounding.
After a lengthy review in which the three officials looked at replays shown on the screen of a laptop computer, it was ruled that the ball left Chen's hand a fraction of a second after time had expired.
Given a second chance, Arizona dominated the overtime period with Lyons converting a pair of 3-point plays.
Lyons finished with 24 points, hitting all 10 of his attempts from the foul line. Solomon Hill added 15 for the Wildcats and Kevin Parrom had 13.
Arizona improved to 13-0 in what was the first Pacific-12 Conference game for both schools. Duke, Michigan and Wyoming are the other unbeaten major college teams left this season.
Colorado, which suffered three missed free throws during the final 1:13 of regulation, slipped to 10-3. The Buffaloes were led by Askia Booker with 18 points.