Making their annual trip to Seattle, Olynyk and the Bulldogs (10-1) controlled the interior and wore down the Wildcats in the second half. Olynyk's highlight was a rattling, one-handed slam with about 9 minutes left that drew a technical foul for screaming, but also gave the Bulldogs a 14-point lead.
Gonzaga outscored Kansas State 38-12 in the paint.
Angel Rodriguez led Kansas State (7-2) with 14 points, but leading scorer Rodney McGruder had a miserable night. McGruder didn't score for the first 30 minutes and finished with four points.
McGruder, who came in averaging 12.9 points, shot 1 for 9 from the floor.
Gary Bell Jr. had 11 points for Gonzaga, which played before its extensive fan base in the Puget Sound region for the 10th straight year and improved to 6-4 in the event. It was a chance for the Bulldogs to erase the disappointment of their last outing a week earlier when defensive lapses and a red-hot Brandon Paul keyed Illinois' 85-74 upset that snapped the best start to a season in Gonzaga history.
There was no lingering hangover from the Illinois loss. Olynyk made 10 of 13 shots, falling just short of matching his career high of 22 points when he fouled out with 4:56 left. Even more impressive for Gonzaga was its domination inside without getting a big game from Elias Harris, who finished with 10 points and seven rebounds.
Kansas State was trying to pick up an early signature win in Bruce Weber's first season coaching the Wildcats. They fell short in their first attempt when they lost to then-No. 4 Michigan 71-57 last month.
After using Guy Landry Edi on McGruder for most of the first half, the Bulldogs stuck Mike Hart on the Wildcats' scoring leader to start the second half. He was immediately flustered, committing turnovers on Kansas State's first two possessions and Gonzaga started the half on a 9-0 run to take a 36-26 lead with 16:28 left.
Kansas State briefly stemmed the run, but Edi's 3-pointer with 12 minutes left pushed the lead to a dozen and Olynyk's dunk that drew the technical capped another 11-2 spurt by the Bulldogs.
Gonzaga's lead reached 21 in the final minutes.
The 3-point shooting that kept Kansas State hanging around in the first half disappeared during the final 20 minutes. The Wildcats shot 1 of 6 on 3-point attempts in the second half. Rodriguez had only two points after the break.
Gonzaga tried to pull away early with a 10-0 run late in the first half to take a 23-17 lead, but led just 27-26 at the break thanks to the shooting of Rodriguez and Will Spradling. Kansas State sustained a big blow late in the half when forward Nino Williams crashed hard to the floor with an apparent right shoulder injury. He was helped to the locker room and did not return in the second half. Williams had two points and three rebounds in 6 minutes.