UTA won its first match in action since Feb. 9 by downing UTEP on Friday in El Paso.
A tiebreaker decided the doubles point as Rice topped UT Arlington on Friday at the UTA Tennis Center.
UTA had two reach consolation finals to join Klara Mrcela's run to the Draw 5 finale at SMU.
Nanaka Takeuchi and Luica Natal look to remain perfect on the season when they head to Dallas.
Lucia Natal went 3-0 to claim her flight at the Rice Invitational in her Maverick debut.