"It was good because we wanted to have some good momentum and the run accomplished that," said Proctor, who spent the last two seasons backing up Ricky Dobbs. "We practiced that play 100 times this summer."
Jon Teague kicked a school-record 54-yard field goal for Navy and Aaron Santiago added two touchdowns on a 13-yard run and 12-yard pass from Proctor.
Delaware, of the Colonial Athletic Conference, came into the game ranked fifth in the Football Championship Subdivision preseason poll after playing in last year's subdivision title game.
He scored twice more on runs of 27 and 1 yards and added his first career touchdown pass.
"With it being my first game as the go-to guy, it was nice to get the monkey off my back," said Proctor, who also scored on runs of 27 and 1 yards and finished his day with a 12-yard pass to Aaron Santiago for his first collegiate scoring pass.
He finished the game with 176 yards rushing and 46 passing, completing 4-of-7 passes.
The Mids finished with 437 yards total offense, 391 on the ground.
"I am proud of this team. Coming in we didn't really know what we had," coach Ken Niumatalolo said. "We had a new quarterback and a young defense going against a talented Delaware team. Our defense played well, our offense played well and we had some good things from our special teams."
Delaware, which played the final quarter without starting quarterback Trevor Sasek, finished with 363 yards, but that included a 78-yard scoring drive against Navy's reserves.
Andrew Pierce ran for 119 yards on 20 rushes. It was Pierce's eighth career 100-yard game.
Sasek, who was injured late in the third quarter when he was tackled hard at the end of a flea-flicker play where he caught a pass, completed 9 of 19 passes for 82 yards and scored on a 21-yard run. His replacement Tim Donnelly completed 7 of 9 passes for 60 yards.
"Without the dropped balls, he could have been something like 12-for-15. Early indications look like there is no structural damage to the knee," Delaware coach K.C. Keeler said.
Santiago's 13-yard run capped a 61-yard drive, following a fumble recovery by Mason Graham.
Teague added a field goal from 36 yards after a Navy drive lasting 8 minutes, 23 seconds.
Sasek's 21-yard run got the Hens on the scoreboard, but Teague's 54-yard kick with the wind at his back gave Navy a 19-7 halftime lead. The old record was 52 yards by Todd Solomon in 1984.
Navy scored on its first possession of the second half on Proctor's 27-yard run for a 26-7 lead.
"That was the Kriss Proctor we have seen for three and a half years. He is a talented kid," Niumatolo said. ''His opening run helped us from the standpoint that we wanted to get out ahead of them and dictate the pace.'
Delaware added a 25-yard field goal by Sean Baner to make it 26-10, but Sasek injured his knee when he was hit hard after catching a pass on a trick play. Sasek returned to quarterback on the next series, but lasted one play before leaving for good.
"He got jammed twice in the same spot. The pain was excruciating," Keeler said. "The first time, he was able to suck it up and go back in. The second time, I said 'You are not even going to try to go back in.'"
Navy added two scores on a 1-yard run by Proctor and a 12-yard pass to Santiago for his first career passing touchdown. Kwesi Mitchell's interception set up the score.
Delaware's final score came on a 1-yard run by Pierce with 2:54 to play.