Jenkins' game-winning shot capped an 11-4 run by the Patriots (2-4) in the final 21 seconds that included a pair of 3-pointers by Patrick Holloway.
Jenkins finished with 24 points and seven rebounds. Holloway added 18 points and Marquise Moore 11.
George Mason trailed 59-53 with 21 seconds to play when Holloway hit two from the line followed by a pair of 3s to bring the Patriots to within one, 62-61.
The Jaspers' Shane Richards went to the line with 2 seconds left, sinking the first shot but missing the second. Jenkins got the rebound and then hit the 3 with a second left to play for the win.
Richards scored 18 points and grabbed four rebounds for the Jaspers (1-4). Tyler Wilson added 15 points and seven assists.