Marvin Jefferson added 13 points and 11 rebounds for the Vandals, who evened their overall record at 14-14 and improved to 7-7 in the Western Athletic Conference.
Sylvester Seay scored 23 points for Fresno State (12-18, 3-11), including a 3-pointer at the buzzer.
Mychal Ladd gave the Bulldogs some life with 1:08 left by stealing the ball in the backcourt and converting a layup to trim Idaho's lead to 69-65.
But following a Vandals turnover, Bryce Cartwright missed two free throws to keep Fresno State's deficit at four.
Hopson sealed the victory by intercepting a Ladd pass at the three-point arc, drawing the foul and making two free throws with 18.4 seconds left. The junior point guard also had 10 assists.
The Vandals shot 52.9 percent from the floor and outrebounded Fresno State 40-31 to overcome 15 turnovers.
Idaho grabbed its biggest lead of the game, 65-54, on Kashif Watson's layup with 6:54 left, forcing a Bulldogs timeout.
The Vandals twice built nine-point margins midway through the second half, helped by two Luciano de Souza 3-pointers.
Paul George's 3-pointer on Fresno State's opening possession of the second half tied the game at 40-40. George finished with 19 points.
Morris went 4-of-4 from three-point range off the bench in the first half for Idaho. His 12 points paced the Vandals to a 40-37 halftime lead.
There were nine lead changes and five ties in the seesaw first half. Idaho shot 61.5 percent compared to 50 percent for Fresno State.