UTEP (11-7, 4-1) trailed the entire second half but tied the game five times before Moore hit a jumper to knot it 65-all with 19 seconds showing.
East Carolina (12-7, 3-3) regained the lead, 67-65, on a Miguel Paul layup with 4 seconds left.
UTEP's Jacques Streeter took the ensuing inbounds pass, dished it off to Moore, who managed three dribbles before pulling up midway between the 3-point arc and half-court line for the game-winner.
It was Moore's third trey and the 14th for the Miners, shattering their previous game-high of nine.
UTEP has won 10 of its last 13 games after starting the season 1-4.
Paul led East Carolina with 20 points, but the Pirates couldn't overcome a 9-of-27 first-half shooting performance.
Purdue coach Matt Painter says players haven't used the fifth-year graduate transfer rule for its true intent.
The dust has settled after players made their NBA draft decisions. Which college teams won? Which lost? Well, Villanova is pretty happy. USC, meanwhile, might not be as thrilled.
The 2017 recruiting class is short on point guards, with Trevon Duval leading only eight prospects from the ESPN 60 who are still available.
|Texas San Antonio||3-15||13||5-27|