Paulius Packevicius was the only player in double figures for Rice (3-12, 0-2) with 13 points.
Jackson's layup started a 14-2 run to finish the first half for the Miners, who led 38-21 at halftime.
Rice was down 18 early in the second half when Culpepper hit a 3-pointer to start a 15-2 run that put the Miners ahead 61-30 with 9:37 remaining.
The Owls were just 5-of-23 from the field (22 percent) in the second half and shot 30 percent for the game.
UTEP guards Julyan Stone and Marvin Kilgore scored just two points apiece, but they engineered the offense by combining for 11 of the Miners' 17 assists against just 15 turnovers.
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