With San Diego State pinned on its 3-yard line thanks to terrific punt coverage by BYU, Adam Dingwell dropped back to pass in the end zone.
Van Noy broke free from the outside and knocked the ball out of Dingwell's hand and jumped on it for the game's first TD.
The play was upheld after video review.
"I wouldn't make those plays if all 11 guys weren't doing what they were doing," Van Noy said. "The ball just happened to land in my lap."
Dingwell fumbled the snap on SDSU's next play from scrimmage and it was recovered by Jordan Johnson at the 14. Jamaal Williams scored on a run up the middle on the next play, BYU's second TD in 17 seconds.
With 6:09 left, Van Noy intercepted Dingwell's pass and weaved 17 yards through traffic and into the end zone. Van Noy was selected the game's defensive MVP.
"He's a fantastic football player," BYU coach Bronco Mendenhall said of Van Noy. "He changed the game for us and was the reason we won."
The Cougars (8-5) won for the sixth straight time against SDSU, a former rival from the Western Athletic and Mountain West conferences. BYU went independent after the 2010 season, when it beat SDSU thanks to a controversial fumble. BYU was making its 12th bowl appearance in San Diego. The first 11 were in the Holiday Bowl, big brother to the Poinsettia Bowl.
San Diego State (9-4), playing in the hometown bowl for the second time in three years, missed the chance for its first 10-win season since 1977 and had its seven-game winning streak snapped.
Dingwell finished with five turnovers, including three interceptions. Four of his turnovers were in the fourth quarter.
As big as the defensive plays were for the Cougars, their punt unit came up huge in pinning down the Aztecs four times in the second half. They downed two punts by senior Riley Stephenson at the 1, one at the 2 and another at the 3. They were among the six punts inside the 20.
Stephenson "changed the game," Mendenhall said. ""And he could have easily been the MVP."
SDSU coach Rocky Long agreed.
"I don't know who got the Most Valuable Player, but I'll tell you who I thought the Most Valuable Player was, was their punter," Long said. "Field position made it tough on the offense."
Stephenson said the Cougars practice pooch punts all the time.
"I get more excited when I launch one 60 yards or so," he said. "But with a defense like we've got, we're going to smash any team we go against.
"A lot of times when you're inside the 50 you can't get ahold of it, you just have to drop it down in the corner and hopefully it stays inside the 10," he said. "It's not much of a kick, but look what it did tonight."
Until Van Noy and Williams scored, the game was a field position struggle.
San Diego State's Eric Pinkins intercepted Riley Nelson's pass and returned it 39 yards for a touchdown in the second quarter but the score was negated by a penalty for blocking below the waist. SDSU ended up punting from the BYU 36.
"I thought blocking below the waist on an interception for a touchdown was the key to the game," Long said. "I really believe if we had scored that touchdown, the momentum would have been in our favor the rest of the night."
James Lark, who started at quarterback for BYU, completed 23-of-42 passes for 244 yards and was intercepted twice.
BYU's Cody Hoffman caught 10 passes for 114 yards and was named offensive MVP.
Dingwell completed 12 of 29 for 144 yards. Adam Muema ran 26 times for 103 yards.
It was over when... BYU scored 20 points in the fourth quarter off turnovers. Kyle Van Noy rushed QB Adam Dingwell in the end zone, recovering a fumble for a TD.
Gameball goes to... Van Noy. He added to his school record with his sixth forced fumble of the season. He also had a blocked punt and iced everything with a pick-six.
Stat of the game... 2. Van Noy scored more touchdowns than anybody on the field. The most valuable defensive player was the most valuable offensive player, too.