Olynyk shot 9 for 9 from the field and 8 for 8 on free throws to go along with nine rebounds, and Harris had 10 boards for Gonzaga (18-2, 5-0), which was coming off a last-second loss at No. 9 Butler last weekend.
Josh Sharp and Brandon Davies led BYU (15-6, 5-2) with 14 points each.
Tyler Haws, the WCC scoring leader at 21 points per game coming in, was held to just one point for the Cougars. Haws had 42 points against Virginia Tech, the most by a Division I player this season. His previous low this season was nine points against Iowa State, and he had scored at least 20 in seven consecutive games coming in.
BYU made only three of its first 16 shots to fall behind 15-8 midway through the first half. Three baskets and a free throw by Harris pushed Gonzaga's lead to 24-12.
The BYU drought continued, and Gonzaga scored 12 straight points for a 36-14 lead.
The Zags led 40-21 at halftime, after shooting 51 percent. Harris and Olynyk had 14 points each in the half.
The 21 points were BYU's lowest in the first half this season. Haws did not score in the first half, missing all six of his shots. The Cougars were shooting just 25 percent (8 for 31) at the break, including just 1 for 10 on 3-pointers. The Zags dominated inside, outscoring BYU 24-8 in the paint in the first half and grabbing eight more rebounds.
The Cougars came out sharper in the second half and their shooting improved, but they couldn't make up much ground.
Brandon Davies scored 10 points as BYU cut Gonzaga's lead to 59-46 with 9 minutes left. But every time the Cougars scored, it seemed that Olynyk or Harris would reply for the Zags.
Gonzaga, which has won three straight against BYU, improved to 114-8 in the McCarthey Athletic Center since it opened in 2004.
Thursday also marked the 125th anniversary of the founding of Gonzaga, and there was a video celebration at halftime that featured basketball alums Ronny Turiaf and Courtney Vandersloot, among others.