Matt Nelson was held to 11 points and 10 rebounds for Colorado State (9-6, 1-1 Mountain West) but extended his string of double-figure scoring games to 13.
Trailing by 10 at the half, the Cougars scored the first six points of the second half and took a 43-42 lead with 10:58 left on baskets by Ainge and Garner Meads. But Smith took over, scoring 13 points over a seven-minute stretch including a 3-pointer with 3:42 remaining to put Colorado State ahead 64-54.
After the Rams missed four free throws, two 3-pointers by Ainge got BYU within 70-67 with 45 seconds left. Two free throws each by Jon Rakiecki and Nelson sealed the game.
The Cougars double-teamed and denied Nelson in the first half, but Colorado State didn't need him in building a 32-22 lead at the half. Morris came off the bench to score four points in a 12-2 run to close the period after Ainge tied the game at 20 with a 3-pointer with 5:48 left.
BYU hurt itself shooting 19 percent and going 2-for-13 over an eight-minute stretch. The Rams overcame 12 turnovers in the first 20 minutes, including ones on their first four possessions, but were near flawless when Morris came on.