UTEP (26-2, 17-0) had just one brief lead in the first, but trailed as much as eight.
Behind Hughes, who went 11-of-21 from the field, the Miners went on a 12-2 run to pull ahead of the No. 9-seeded Owls (14-18, 6-11).
Rice jumped out to a quick 14-6 lead at 12:14 in the first, and UTEP shot an abysmal 12-of-31 from the field for a team averaging 32 points in the first half.
Hughes had just four points in the first, hitting only one field goal. The sophomore guard then scored 28 of her 32 in the second half, including going 11-of-11 at the free throw line, but was 0-for-6 from three-point range.
UTEP drastically improved shooting in the second, shooting 60 percent on field goals. Center Izabela Piekarska contributed 14 points and guard Kasia Krezel added 12 on 5-of-7.
The Owls struggled in the second, committing 13 turnovers and shooting poorly against a Miner defense that had eight steals and three blocks. Rice didn't improve from the first, going 10-0f-29 from the field and a mere 35 percent for the game.
Kadie Riverin led the Owls, scoring a team-high 23, and Valeriya Berezhynska added 16 and eight rebounds. Maudess Fulton also had 15.
UTEP had never been ranked in the Top 25 prior to Feb. 11, nor has it advanced past the semifinals of its conference tournament.