Tom Smart, Deseret News
Brigham Young Cougars guard Tyler Haws (3) as they play men's basketball in the second round of the NIT on Monday, March 25, 2013, in Provo.

PROVO — Amid a season that has seen BYU produce its share of inconsistent performances and experience plenty of disappointing moments, the Cougars seem to be playing their best basketball right now.

And BYU has an opportunity to finish the checkered campaign with a flourish by advancing to the National Invitation Tournament Final Four at historic Madison Square Garden in New York City.

The No. 3 seed Cougars are one victory away from grasping that prize.

But standing in their way is No. 1 Southern Miss, which hosts BYU Wednesday (6 p.m. MST, ESPNU) at Reed Green Coliseum in an NIT quarterfinal matchup.

No doubt, pulling an upset on the road against the Golden Eagles will be a tall order for the Cougars. Southern Miss finished second to Memphis in the Conference USA standings this season.

"We are going to give our best effort and try to keep playing," said BYU senior Brandon Davies, who scored a game-high 26 points and pulled down 10 rebounds in Monday's 90-71 second-round victory over Mercer at the Marriott Center.

Not only do the Cougars have little time to prepare for Southern Miss, but they also have had to deal with traveling a long way. After Monday's win, BYU players and coaches arose early Tuesday to catch a flight to Hattiesburg, Miss.

There, BYU will play in front of what's expected to be a hostile crowd.

"If (Monday’s environment) was a 9.5, we need Wednesday to be a 10," first-year Southern Miss coach Donnie Tyndall said after his team's 63-52 win over Louisiana Tech on Monday before 5,922 rowdy fans. "It was a great environment. This was a big-time college basketball game with a lot at stake."

And Wednesday's game will have even more at stake, including a trip to the Big Apple.

BYU won the NIT back in the tournament's heyday in 1951 and 1966. The Cougars have come close to reaching Madison Square Garden a couple times since. In 1986, BYU won two NIT games before falling at Ohio State. In 2000, the Cougars beat Bowling Green and Southern Illinois, then fell at Notre Dame.

Southern Miss, meanwhile, boasts its own impressive tournament history, having claimed the NIT championship in 1987.

BYU played a pair of games at the Barclays Center in Brooklyn, N.Y., last November, losing to Florida State and Notre Dame. The Cougars would love to return to New York City for the NIT Final Four.

"That was definitely a highlight of the season, going back to play in the Barclays Center," BYU guard Tyler Haws said last week. "It was a great experience. We want to get back to New York and play in Madison Square Garden."

Of course, Southern Miss would also like to ease the pain of not getting into the NCAA tournament by going to the NIT Final Four.

For BYU, the Golden Eagles will be a challenge to stop, as they rank No. 11 in the nation in shooting.

"Southern Miss is a really good offensive team," said Cougar coach Dave Rose. "They shoot (nearly 40 percent) from the 3-point line. They shoot 48 percent from the field. They're very athletic. They like to change defenses, change it around."

The Golden Eagles' starting five is comprised entirely of junior college transfers, including two seniors and three juniors. Senior forward Dwayne Davis averages a team-high 16.3 points per game, while junior guard Jerrold Brooks averages 10.9.

The Cougars have marched to the NIT quarterfinals thanks to the outstanding, consistent play of Davies, Haws and Matt Carlino.

BYU will need more of the same — this time on the road — if it is to extend its NIT run, and its season, to New York City.