Rice (6-3, 5-1 Conference USA) clinched bowl eligibility for the second time in three seasons. Not since 1960 have the Owls been 5-1 in conference play.
Clement threw three touchdowns to James Casey, who finished with 12 catches for 142 yards, and one each to Jarett Dillard and Pierre Beasley.
Vittatoe threw for 265 yards and helped UTEP build an early 17-7 lead in the first quarter before the Owls lurched back to go up 28-20 by halftime.
Moturi finished with five catches for 109 yards.