The Saints recovered an onside kick and narrowed the margin to 40-31 on a Ballinger pass to Ivan Zavala.
Then the defense picked up. Josh Covert had 22 tackles and an interception in the game.
Ballinger, who played wide receiver as a freshman and sophomore, caught the first touchdown pass of his career from Zavala after lining up in the Wildcat formation to make it 40-38.
"It was kind of cool to get my first touchdown that way," Ballinger said.
The defense made a goal-line stand, and the team was 95 yards away from history. The Saints converted a couple of fourth downs to put them in striking distance.
Ballinger threw his sixth touchdown of the game on a 36-yard pass to Zavala that caused the celebration penalty.
"I got tackled after I threw the ball," Ballinger said. "I heard people screaming and looked up in disbelief. Best penalty ever."
Zavala had seven catches for 178 yards and three touchdowns. Luna finished with five receptions for 231 yards and three scores.
"That was for Coach Cartmill," Ballinger said. "He's the one that started it off. Give credit to the past teams that helped us get here. That was history for us, what a great feeling. That's what football is all about."