Second-year coach Stoffel can also thank quarterback Noah Reed for his first win in the annual rivalry.
"Our quarterback decided that he wanted to be a quarterback tonight," Stoffel said. "He played like he's capable of playing. He used his speed, his mind and arm. He did what he was supposed to do with the ball in our offense."
Reed finished 12 of 16 for 112 yards and three touchdowns while rushing for 61 yards on six carries.
"This was a huge win and huge boost of confidence," Reed said. "We had a good, complete game. Everyone played hard and never gave up. I'm so proud of our team. I hope it leads into next week and we will see what happens from there.
All three of Reed's touchdown passes came in the fourth quarter, connecting with Dakota Kelly on a 1-yard pass, Jeffrey Seams on a 3-yard pass and David Reed on a 6-yard pass.
The only lead the Wildcats held in the game was a 10-7 halftime lead after a Brayden Underwood 23-yard touchdown run.
Underwood finished with 102 yards on 22 carries and a touchdown while quarterback Tyler Barton finished 14 of 35 for 242 yards.