Air Force built a 33-24 lead at the break, and eliminated any chance for a late Austin Peay rally by winning the second half scoring output, 42-27.
Tim Anderson led the way with 13 points, eight rebounds, and six assists.
Matt McCraw had 13 points and eight rebounds; Dan Nwaelele had 13 points and four rebounds; while Nick Welch and Jacob Burtschi were the other players with 13 points for the Falcons (24-8), who broke a four-game losing streak.
Fernandez Lockett was the only player to score in double figures with 17 points for the Governors (21-12), who closed their season by losing three of their final five games.
Air Force will face Georgia Monday night in the second round.