Dion Dowell added 19 points and 14 rebounds for the Cougars, whose 23-9 record is their best since the 1991-92 season. They advance to the second round Monday against the winner of Wednesday's game between Washington and Valparaiso.
"The style of game I thought was exciting, on national television. I think it is a great start for the CBI," said Penders, whose team accepted a CBI invitation on Sunday without knowing yet whether the NIT was interested.
"I think we were the first team to make the commitment. We made it because we felt this is a cutting edge tournament. It's going to be really special," he said.
"That is not a knock on the NIT. It's a great tournament. ... But we felt like this is going to be a tournament of the future where they are just going to try to get the best teams and take all the politics out of it."
"We think in three or four years this is going to be the answer to everybody who says we don't have enough teams in the NCAA tournament," said Penders, who now has a record of 607-409 in 34 years of college coaching.
Armon Johnson missed a 3-point attempt at the buzzer for Nevada, which had trailed by as much as 10 points the second half and closed its sixth consecutive year of postseason play at 21-12.
Marcelus Kemp led Nevada with 24 points, six rebounds and five assists. Johnson had 16 and Brandon Fields 15.
"I'm real proud of the way we played. We just came up a point short," Nevada coach Mark Fox said. "They (the Cougars) are an excellent offensive team, excellent shooting team."
Tied at 71, Dowell followed a pair of free throws with a tip-in to put Houston ahead 75-71 with 3:10 left. The Cougars went up 79-75 on Kelvin Lewis' floater in the lane at 1:50.
JaVale McGee, who scored Nevada's first 6 points of the game on three slam dunks but fouled out with 12 points total, scored inside but missed the free throw when he was fouled at 1:33. After McKiver missed a 3-pointer, Kemp scored inside to make it 79-79 with 58 seconds left.
Houston led 43-36 at the half on Tafari Toney's 35-foot bank shot at the halftime buzzer. The Cougars made 14-of-35 3-point attempts on the game, including 13 of their first 24.
"They were hot from the three (point range) in the first half," Fox said. "At the end of the first half, they bank one in. It's the difference in the game."
The Cougars took their biggest lead, 50-40, on Lewis' 3-pointer with 17:44 remaining. But Nevada answered with a 20-5 run to take a 60-55 lead on Kemp's 10 footer at 10:55. That run included a 10-0 stretch started by DeMarshay Johnson's slam dunk off a behind-the-back pass from McGee in the lane.
McKiver's two free throws and 3-pointer pulled Houston to within 61-60 at 9:26, and Lewis' basket off a rebound tied it at 71 with 4:31 left.
Penders said his team was "just very fortunate to win against an outstanding club."
"I'm not blowing smoke when I say this. We've played a lot of NCAA tournament teams. They're an NCAA tournament-type team. They have had a lot of tough breaks this year themselves, like we have," he said.
"We've lost like six games by a total of 26 points and four in the last 2 or 3 seconds of the ballgame. So we feel like we've got a real outstanding ball club, and a bunch of guys who really fight."