Marcus Capers added 12 points for Washington State (8-2). The Cougars relied on superior rebounding and a big free throw advantage to stay ahead of the Falcons.
Michael Lyons had a career-high 25 for Air Force (5-3). Grant Parker, who leads Air Force with 17 points per game, did not suit up because of a groin injury.
Washington State made 19 of 25 free throws, while Air Force made 11 of 13. The Cougars also had a 36-24 rebound advantage.
After leading 31-24 at halftime, Washington State scored nine-straight points early in the second half -- including back-to-back 3-pointers by Moore and Thompson -- for a 40-26 lead.
Lyons scored seven consecutive unanswered points as Air Force pulled within 42-35 with 13 minutes left.
The teams traded baskets until Air Force scored seven straight behind Tom Fow's basket and 3-pointer to cut WSU's lead to 57-55 with a little less than 7 minutes left.
But Capers scored seven-straight points as WSU rebuilt a 66-57 lead with 5 minutes left. Air Force could not make up the difference.
Washington State led 31-24 at halftime thanks to 46 percent shooting and a 19-13 rebounding advantage. Air Force shot just 39 percent in the first, including 2 of 13 3-pointers and did not shoot a free throw.
This game was played in the Spokane Arena, 70 miles north of the WSU campus in Pullman, to satisfy NCAA requirements that WSU officials put on a game at least once this season in the building where the school will host a portion of the NCAA men's basketball tournament in March.
The teams have played just once before, with WSU winning in 2007, also in the Spokane Arena.