Memphis accomplished feats not seen from its program in decades but will have to get past a veteran of the bowl season to end its breakthrough campaign with a victory.
BYU will make its 10th consecutive postseason appearance Dec. 22 in the inaugural Miami Beach Bowl.
After going 3-9 in 2013, Memphis went 9-3 to finish with its most wins in the regular season since 1963, and it has a chance to tie the program record of 10 victories set in 1938.
The Tigers earned a share of their first league title since 1971 by finishing 7-1 in the American Athletic Conference and are riding a six-game win streak - their longest in one season since a seven-game run in 1969.
They'll make their first postseason appearance since a 41-14 loss to South Florida in the 2008 St. Petersburg Bowl.
"For us right now, it's about finding a way to win a championship, which for us is the bowl game,'' third-year coach Justin Fuente said. ''We won't focus on the number 10. We'll focus on the number one. Can we go 1-0 this week? That's kind of what we've talked about each week for the last six weeks."
The Tigers, 3-3 all-time in bowl games, haven't won one since edging Akron 38-31 in the 2005 Motor City Bowl and will have their first matchup with a BYU program that's won six of its last eight postseason games.
The Cougars (8-4) won a school-record four consecutive bowls before a 31-16 loss to Washington in the Fight Hunger Bowl last December. They had a streak of 17 straight postseason appearances from 1978-1994, including a Holiday Bowl victory over Michigan in 1984 that secured their lone national title.
They'll carry a four-game win streak into this appearance and totaled 148 points in the final three victories. BYU ranked 19th in the FBS with 36.2 points per game and 25th with an average of 462.5 yards.
"It could be a really nice finish, I think, for either team to finish with one more win," coach Bronco Mendenhall said.
Christian Stewart threw for 1,281 yards and 14 touchdowns with one interception during the win streak. The senior and former walk-on took over after Taysom Hill suffered a season-ending injury in a 35-20 loss to Utah State on Oct. 3, the first of four consecutive defeats.
Stewart and the Cougars will face a Memphis team that's fifth in the nation with 17.1 points allowed per contest and 22nd with an average of 343.3 yards allowed.
"They are well coached with a strong defense and a balanced offense. It should be a great matchup," Mendenhall said.
In its 10 games against unranked teams, Memphis' averages dropped to 13.9 points and 315.3 yards allowed. The Tigers' two defeats to AP Top 25 foes came at UCLA on Sept. 6 and at Mississippi on Sept. 27, but they also lost 28-24 on Oct. 11 to a Houston team that BYU beat 33-25 exactly one month earlier.
BYU and Memphis had two more common opponents in Connecticut and Middle Tennessee State, and both teams earned notable wins over each school. The Tigers beat UConn 41-10 on Nov. 29 to clinch a share of the AAC title, and BYU topped MTSU 27-7 on Nov. 1 to start its current win streak.
Senior linebacker Bronterrious "Tank" Jakes was named the AAC's co-defensive player of the year after leading Memphis with 85 tackles - a conference-best 15 1/2 for loss - and six sacks.
Brandon Hayes needs 100 yards to become the Tigers' first 1,000-yard rusher since Curtis Steele in 2009, while Paxton Lynch needs 275 yards to become their first with 3,000 passing since Martin Hankins in 2007. His 18 TDs are the most since Hankins' 25 that same year.