Joey Shaw added 16 points and 12 rebounds for the Wolf Pack (15-9, 7-4 Western Athletic).
Ike Okoye led Boise State (11-14, 2-10) with 32 points. Daequon Montreal added 18, including a 3-pointer with 11 seconds left in regulation that sent the game into overtime tied at 73.
In the extra period, Nevada led 77-76 with 3:19 remaining before going on a 10-2 run to put the game away. Babbitt had eight of the 10 points in the run, sealing the win with a pair of free throws with 51.8 seconds left.
Boise State led the entire first half, building a nine-point lead in the first five minutes en route to a 34-28 advantage at the break.