BOISE, Idaho (AP) -- In a game with 136 total points and nearly 1,300 yards of total offense, it was the defense that made the biggest play.

Sooner or later the defense had to make a stop, and Boise State's Tim Brady did just that on the final play in the fourth overtime period, stuffing a 2-point conversion attempt in a thrilling 69-67 victory over Nevada on Sunday night.

The game set a record for most points in an NCAA Division I-A game since 1937, when official record keeping began.

The shootout finally ended on a sack by Brady, foiling Nevada's attempt to send the game into a fifth overtime.

"It was the biggest play we had all night," Boise State coach Chris Petersen said. "It's really too bad someone had to lose this one. I don't think I've felt that way after any game, ever."

For a while, it seemed this one would never end -- not with the way the offenses were moving up and down the field.

The Broncos (5-1, 2-0 Western Athletic Conference) rolled up 627 total yards on offense, including Ian Johnson's 205 yards rushing and three touchdowns.

Nevada, led by Colin Kaepernick, a redshirt freshman quarterback making his first start, topped the Broncos with 639 total yards. The Wolfpack (2-4, 0-2) tied the game in the fourth extra period when Luke Lippincott scored on an 8-yard burst up the middle, capping a rushing attack that amassed 406 yards, the fourth most ever allowed by Boise State.

But Nevada opted to pass on the two-point try, and Kaepernick rolled right, found nobody open then moments later found himself in Brady's grasp, sealing Boise State's eighth straight win over the Wolfpack.

"To come up two points short in overtime in a game like this is a hard pill to swallow," said Kaepernick, who threw for three TDs and rushed for two more. "We knew we were going to have to keep putting points on the board to stay in the game."

Talk about an understatement.

Altogether, the teams combined for 17 touchdowns, 1,266 total yards of offense and a handful of personal bests.

Boise State quarterback Taylor Tharp threw for a career-high 320 yards and four touchdowns. Two of those came in the first two overtimes, both 25-yard scoring strikes to Jeremy Childs and Sherm Brasser.

Johnson had 256 yards total offense, including a 32-yard TD pass, the first of his career in the fourth quarter that put the Broncos up 41-34. His 72-yard TD run in the second quarter was the longest of his career.

Kaepernick, starting in place of injured sophomore Nick Graziano, ran for 177 yards and two scores and passed for another 243 yards and three TDs. His performance came against a Boise State defense that entered the game the third best in the nation, averaging just 12.2 points per game.

"I'm proud of our guys," Nevada coach Chris Ault said. "They came back and stood up all game long. We're going to learn a lot from this game and get better."

The Wolfpack trailed most of the game, but grabbed their first lead late in the fourth when Brett Jaekle made a 35-yard field goal.

But Boise State freshman Kyle Brotzman sent the game into overtime by nailing a 27-yard field goal as time expired.

The teams traded touchdowns through the first two overtimes. In the third, Jaekle put Nevada on top with a 27-yard field goal, but Brotzman answered with a 29-yarder.

In the fourth overtime, Johnson scored from a yard out and Tharp lofted a short pass to Jeremy Avery on the 2-point conversion.

Nevada matched the touchdown, but Brady came up big when he got back up on his feet and chased down Kaepernick to end the game.

"You've got to give a lot of credit in this game to our offense," Brady said. "They battled for us and they kept us in the game because we weren't on top of our game tonight."