PROVO, Utah (AP) -- The celebration over Brigham Young's first conference championship in five years wasn't over until Elvis sang. Actually, it may have been just beginning.

No. 23 BYU clinched the Mountain West Conference title with a 42-17 win over New Mexico on Saturday, leaving only one opponent left between the Cougars and a perfect conference season.

"It's a great day for our program and a great day for these young men," said BYU coach Bronco Mendenhall, who has returned the Cougars to the top of the Mountain West in less than two seasons.

The Cougars (9-2, 7-0) held a long and boisterous celebration at midfield after the game, with the seniors taking turns at the microphone before Elvis' "Viva Las Vegas" blared from the stadium loudspeakers and athletic director Tom Holmoe accepted a bid to the Las Vegas Bowl as the MWC champions.

It's the 22nd conference title at BYU.

Curtis Brown ran for 124 yards and became the leading rusher in BYU history and John Beck passed for 464 yards and four touchdowns for the Cougars, who won their eighth straight.

"There was a lot of doubts and questions when Coach Mendenhall took over. Hey, if there's doubts or questions now I don't know what team you're watching," Brown said. "This team is full of confidence, full of swagger. We're just ready to go out there and win every game."

Beck completed 28 of 42 passes with two interceptions and became the second Cougar to pass for 10,000 yards. Brown had 13 carries for 124 yards, including a 49-yard touchdown run in the first quarter, and also caught a 9-yard touchdown.

BYU led 28-3 and put New Mexico away after allowing two quick touchdowns in the third quarter. Quincy Black returned an interception 88 yards for a touchdown for New Mexico (5-6, 3-4), but the Lobos couldn't stop Beck and Brown in their final game at LaVell Edwards Stadium.

Chris Nelson completed 22 of 38 passes for 245 yards, but also had two interceptions. Rodney Ferguson ran for 138 yards on 20 carries for the Lobos, who need to beat San Diego State next week to be eligible for a bowl.

New Mexico finished with three turnovers.

"I thought the way our offense was playing, if we don't turn the ball over, it could have been one of those shootouts," New Mexico coach Rocky Long said. "We weren't even slowing them down, so it would have been who could score the most points. But when you turn the ball over ... it's hard to stay in a shootout."

All that's left for BYU is state rival Utah, which has one the last four meetings against the Cougars. Rather than wait, Mendenhall gave the OK to start celebrating the bowl berth with one regular-season game left.

"I figured we might as well acknowledge it and get it over with now rather than having it hanging over our heads for a week," Mendenhall said.

The Cougars finished with 653 yards of offense and punted only once while finishing a perfect home season.

After stopping New Mexico on an incomplete pass in the end zone, the Cougars let the clock run out, but had to wait a few minutes for security to clear the field so Mendenhall and his Cougars could receive their first MWC championship trophy in five years as the remaining fans chanted "B-Y-U!"

"What felt good was seeing the excitement in our players' eyes and to see them smiling," Mendenhall said.

BYU hasn't trailed since a double-overtime loss at Boston College on Sept. 16. The Cougars kept that streak alive with two touchdowns in the first quarter, starting with Brown's 49-yard run just 2:07 into the game.

Brown needed 38 yards entering the game to tie Jamal Willis' school record of 2,970 yards, set from 1991-94. He had one rushing yard before breaking free up the middle and going into the end zone untouched.

Brown credited the BYU backs who preceded him.

"They paved the way," he said. "They established the running game and all I did was add to it."