Kelly Olynyk scored 21 for Gonzaga (12-1), Elias Harris had 17 and Gary Bell Jr. added 12. The Bulldogs shot 52 percent from the field on 31 of 59 shooting. Pangos made 10 of 13 shots and finished two points shy of his career-high.
Pierre Jackson led Baylor (8-4) with 26 points, Isaiah Austin, a 7-foot-1 220-pound freshman, had 20 and Cory Jefferson added 13. The Bears also shot 52 percent for the game, but attempted 21 fewer free-throws than Gonzaga.
Gonzaga didn't hold a lead until the 4:53 mark of the first half. But once they got the lead, they were determined not to relinquish it. The Bulldogs never trailed after halftime and led by as many as 12.
Gonzaga drew two quick fouls on Austin after halftime and he went to the bench with three fouls. Harris' bucket and free-throw made it 47-38 Gonzaga.
Baylor made its first three 3-point attempts of the second half, two by Jackson, and cut the deficit to 49-44. Jackson entered the contest as the scoring leader in the Big 12, averaging 19 points and 6.3 assists.
Pangos' second 3-pointer of the second half extended Gonzaga's lead to 62-50 with 12:12 left. Pangos and Olynyk combined to score 15 straight Gonzaga points over a five minute span.
Jackson and Austin made back-to-back 3-pointers and Baylor stayed within reach at 62-56. Austin showed off his versatile skills, making shots from inside the paint, outside the 3-point line and mid-range jumpers.
Taurean Prince scored four quick points and drew a charge, leading to a Austin jumper on the other end and Baylor pulled within five with 9:39 left.
Baylor didn't get any closer.
Gonzaga's defense did not allow a Baylor run of more than five points over the final 10 minutes of the game.
The first half was a different story as Baylor jumped out to a 8-2 lead in the opening minutes of the game. Gonzaga made three consecutive 3-pointers to tie the game at 13. Jackson scored six straight points for Baylor and the Bears pushed their lead to 24-18.
A Gary Bell Jr. floater in the lane gave Gonzaga its first lead of the game at 30-28 with 4:53 remaining in the half. Bell's bucket sparked a 9-0 Gonzaga run.
Austin's baseline jumper ended a four minute scoring drought for Baylor and cut Gonzaga's lead to 34-30 with 3:28 left. Gonzaga led 38-33 at the break.
Gonzaga made five 3-points in the first half and attempted nine more free-throws than Baylor. The Bears shot 48 percent and the Bulldogs made 12 of 30 shot attempts.
The Gonzaga crowd wasn't its usual rowdy self, partially because most of the students were away during semester break. Gonzaga is 112-8 in the McCarthey Athletic Center.
Earlier this month, Baylor ended Kentucky's 55-game home winning streak at Rupp Arena.
Baylor was Gonzaga's fourth matchup against a Big 12 Conference school this season. The Zags have defeated West Virginia, Oklahoma and No. 25 Kansas State. Gonzaga travels to Stillwater on Monday to face No. 22 Oklahoma State.