The Aggies have now won 32 straight home games -- the third-longest active home winning streak in the nation behind Duke (36) and Kentucky (34).
The win avenges a 78-72 loss last November in Provo.
Noah Hartsock, playing with a bloodied nose, led BYU with 18 points as the Cougars began life without national player of the year Jimmer Fredette.
The game marked the return of center Brandon Davies, who was dismissed from BYU's team in March for violating the school's honor code just as the Cougars had climbed to No. 3 in the polls.
Davies started slow but finished with 13 points.
Friday's meeting was the 228th meeting between the teams but the earliest ever.