The Cougars will learn their NCAA postseason fate when the bracket is announced during the NCAA Tournament Selection Show, airing live at 5 p.m., Sunday, on CBS.
Details about tickets, hotels and other pertinent information will be available at UHCougars.com as soon as possible after the NCAA Tournament Selection Show on Sunday evening.
National scoring leader Aubrey Coleman struggled through a 4-for-20 shooting performance for the seventh-seeded Cougars (19-15), but came up with a critical steal and fast-break layup in the final minute as they won their fourth game in as many days.
Houston trailed by nine with 8 minutes to play, but came roaring back against the top-seeded Miners (26-6), who were riding their longest winning streak since their "Glory Road" run to the national title in 1966.
Randy Culpepper scored 20 points and Derrick Caracter added 18 for UTEP, which was outscored 15-3 down the stretch to lose for the first time since being beaten by the Cougars on Jan. 13.
Lewis hit the go-ahead 3-pointer from the right wing with 3:14 remaining, and Caracter threw the ball away into the backcourt before Adam Brown hit another 3 to make it 74-70.
Caracter bounced back with a basket inside to cut the deficit to two, but Coleman denied UTEP's chance to tie with his steal and layup with 54.4 seconds left. Zamar Nixon took the ball away from Culpepper on the Miners' next possession, setting up a fast-break layup for Brown, and the Cougars were able to hold on from there.
Houston coach Tom Penders brought his team to Tulsa with the approach that the most dangerous man in a fight was the one with nothing to lose. After his team won four games in a row for the first time all season, he's headed to the NCAA tournament with a fourth school, joining an elite fraternity of coaches that includes Rick Pitino, Eddie Sutton and Lon Kruger.
He built a team that takes care of the ball - with the nation's second-fewest turnovers and best turnover margin - and apparently saves its best for last.
The Cougars scattered all over the floor when the final buzzer sounded, jumping up and down in celebration. Coleman eventually splayed out on the court, wagging his right index finger at a television camera that hovered over his head.
Coleman finished with 13 points, half his best-in-the-nation average and his second-lowest total this season, but it didn't matter. Houston ended up with 12 3-pointers, one more than it did in beating UTEP the last time, and was 7 for 12 from behind the arc in the second half. Nixon added 13 points off the bench.
Arnett Moultrie had a pair of two-handed dunks during a 15-6 run by UTEP after the Cougars had rallied back from a seven-point deficit to tie it early in the second half. Moultrie's tip-in of Caracter's missed jumper pushed the Miners' lead to 63-54 with 9:16 left.
Lewis led the Cougars back, sinking back-to-back 3s during a run of eight straight points, and Coleman split a pair of free throws on consecutive trips to get Houston within 65-64 with 5:14 remaining.
Claude Britten, stepping in after Caracter picked up his fourth foul, hit four straight free throws to stem the tide for the Miners - but Houston still had one last surge left.