Kocur's final trey, with 43 seconds left, put the Falcons (12-13, 5-9 Mountain West) ahead 71-66.
The Runnin' Rebels (14-11, 5-7) missed the next shot but scored on their final four possessions, including Christian Wood's 3 at the buzzer. First Air Force made just 1 of 4 free throws as UNLV crept closer before Olesinski made two with 10 seconds left and Matt Mooney sealed it with two at four seconds.
Wood, who made three of the final four buckets for UNLV, finished with a career-high 31 points and Patrick McCaw had all of his career-high 20 in the second half. The Rebels were without leading scorer Rashad Vaughn (17.8), who suffered a torn meniscus in his left knee in Tuesday's 73-61 win over Fresno State.