LAS VEGAS (AP) -After four years spent setting every major passing record for his school, it took three final touchdowns and plenty of long throws Saturday night for Arizona's Willie Tuitama to prove himself a winner.

''Nobody has endured more - well, maybe me - in the last four years,'' Arizona coach Mike Stoops said after the senior quarterback led the Wildcats to a 31-21 win over No. 17 BYU.

''He'll go down in history at Arizona. His legacy is forever etched,'' Stoops said.

Tuitama finished 24-for-35 for 325 yards and two touchdowns, leading Arizona to its first bowl win in 10 years. He added a 6-yard touchdown run in the third quarter to give the Wildcats a 31-14 lead.

''We had a goal before the season started and tonight we finally reached it,'' Tuitama said. ''I'll never forget to finally be in a bowl game with this group of seniors, on this team.''

Arizona fans trickled onto the field as the last minute ticked off the game clock, then sprinted to midfield in celebration of the school's first bowl victory - and winning season - since 1998, when it finished 12-1 and beat Nebraska in the Holiday Bowl.

Mike Thomas caught a 3-yard pass on the final play of the game to give him the Pac-10 career receptions record with 259.

Arizona handed BYU a tough end to a disappointing season for a team that spoke of making a BCS game at the beginning of the year.

''Ten and three is a solid season, but the standards here are much higher,'' BYU coach Bronco Mendenhall said. ''Our standards here are to win the conference championship and be on the national stage.''

The Wildcats (8-5) kept the ball in the air most of Saturday night. Tuitama threw a 71-yard pass to Terrell Turner that set up the first score, a 37-yard touchdown to Delashaun Dean that gave the Wildcats the lead for good, and a 24-yard strike to Chris Gronkowski that sent Cougars fans toward the exits.

The Wildcats stifled BYU quarterback Max Hall throughout the game, forcing him to scramble often, lose two fumbles and throw an interception.

''We had to go with physical tackling - we had eight guys in the box at all times,'' linebacker Xavier Kelley said. ''We had our ups and downs, and this is tremendous. It's amazing, amazing.''

BYU (10-3) lost its bid to win three straight Las Vegas Bowls in four consecutive trips, ending a sloppy night with three missed field goals and 10 penalties for 76 yards.

''It was a good season, but not a great season,'' Hall said. ''We just hit a lull as a team.''

The penalties twice cost BYU prime chances to tie or take the lead. Three straight flags just before halftime turned a third and 1 at the Arizona 19-yard line into a third and 16, and Mitch Payne ended the drive by missing a 40-yard field goal wide left. Arizona led at halftime 10-7.

''Championship coaches don't coach a team to do that. I could have done a better job,'' Mendenhall said. ''We were pressing.''

The Cougars took their first lead of the game in the third quarter after Arizona lost a fumble at its own 29 on the first play of the half. BYU marched to the 1 with five running plays and Max Hall completed a play-action touchdown pass to Andrew George to put BYU up 14-10.

Nic Grigsby 's 1-yard run on Arizona's first possession was set up by Turner's 71-yard catch. Turner cleared BYU's defense on the long pass play but was tackled from behind by Brandon Bradley just short of the end zone.

Grigsby fumbled deep in BYU territory on the next drive, turning the ball over at the 5 and ending a 62-yard drive without a score. But BYU fumbled on its next possession, resulting in a 31-yard field goal for the Wildcats.

BYU scored its first points midway in the second quarter, when Harvey Unga scampered into the end zone from the 1-yard line. Hall completed passes of 35 and 36 yards on the drive, including one to Austin Collie that gave the Cougars a first down on Arizona's 3-yard line.

Collie finished with 119 yards receiving, tying the NCAA record with 11 consecutive 100-yard games.