Vaughn's 3-pointer with 1:06 left put the Rebels in the lead for good at 60-57, but Angelo Warner made a pair of free throw to pull the Eagles within one.
Morehead State forced a shot clock violation to get the ball back with 11 seconds left. But Warner missed on his go-ahead attempt and Chris Wood secured the rebound and the win.
Vaughn also grabbed seven rebounds in his collegiate debut and Christian Wood had 12 points and 12 rebounds.
Warner had 21 points to lead the Eagles, who took the lead late in the first half and extended to 44-33 early in the second.
Wood's free throws put the Rebels up 49-47 with 8:31 remaining and UNLV never trailed again.