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.
After a season that saw his shooting numbers slip, should Nigel Hayes return for his senior year at Wisconsin or take the gamble to put him name in this year's NBA draft?
Isaiah Taylor talks about his decision to declare for the NBA draft and what he will miss most about Texas.
Chattanooga women's basketball coach Jim Foster has received a one-year contract extension, the same day the school gave the men's coach a two-year extension.
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