Keenum completed 30 of 46 passes to help Houston improve to 5-0 overall and 1-0 in Conference USA. The Cougars are 5-0 for the first time since 1990 and only the fourth time in school history.
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Houston had 710 yards on total offense and UTEP (2-3, 0-2) had 538.
Keenum had 489 yards of total offense to move within 421 yards of the NCAA career record of 16,910 set by Hawaii's Timmy Chang. Keenum has 16,489 yards (15,591 passing, 898 rushing). Keenum also moved into a tie with former BYU star Ty Detmer for third place in NCAA history with 121 career touchdown passes.
Sims had 12 carries and two rushing touchdowns -- 40- and 4-yard runs in the second quarter -- and finished with two catches for 90 yards. Michael Hayes added 100 yards rushing on 10 carries, scoring on a 71-yard run late in third quarter to give Houston a 38-28 lead.
Patrick Edwards led the Cougars in receiving with eight catches for 144 yards.
UTEP's Joe Banyard ran for 240 yards -- the fourth-most in school history -- and a touchdown on 22 carries, and Nick Lamaison completed 19 of 29 passes for 267 yards and three touchdowns.
Banyard had a 68-yard touchdown run with 1:02 left in the third quarter to pull the Miners within three at 38-35. Houston's Matt Hogan made a 29-yard field goal early in the fourth, Keenum added his 84-yard scoring strike to Sims with 9:42 left and connected with Justin Johnson on a 2-point conversion to make it 49-35.
UTEP cut it to seven on Leilyon Myers 2-yard run with 6:21 to go. The Miners had a chance to tie it or take the lead, but Mike Edwards failed to control Lamaison's fourth-down pass in the end zone with 54 seconds left.
After UTEP took a 14-0 lead in the first quarter on Nathan Jeffrey's 22-yard touchdown catch and 10-yard scoring run, Houston scored three touchdowns in a 2:31 span in the second quarter. Charles started the spree with his 40- and 4-yard scoring runs and Marcus McGraw returned a fumble 34 yards for the third TD.
UTEP tied it on Mike Edwards' 21-yard touchdown catch with 45 seconds left in the half.
Hogan opened the third quarter with an 18-yard field goal, but UTEP regained the lead at 28-24 on Chris Wenrick's 29-yard touchdown catch. Houston countered with Keenum's 23-yard scoring pass to E.J. Smith to take the lead for good at 31-28.