The Falcons (16-5, 4-3 MWC) led by 12 points midway through the second half but San Diego State put on a late charge that produced a 66-66 tie.
J.J. O'Brien fouled Lyons with 1 1/2 minutes to go and Lyons sank two foul shots to put the Falcons (16-5, 4-3 MWC) ahead to stay.
Todd Fletcher added 13 points and five assists for Air Force, which improved to just 3-78 all-time against ranked teams.
Jamaal Franklin notched 25 points and six assists for the Aztecs (16-5, 4-3 MWC).
Notable deaths of 2014 [PHOTOS]