Renfree passed for 314 yards, threw for a touchdown and ran for two more scores, and Duke nearly blew a 24-point lead before beating Navy 34-31 on Saturday.
The Blue Devils (2-6) snapped a six-game losing streak, but led 34-15 with 8:48 left after a 40-yard field goal by Will Snyderwine.
Navy closed to 34-31 with 2:34 to play when Dobbs hit Aaron Santiago with a 12-yard touchdown pass, then found Santiago again for the 2-point conversion. The Midshipmen (5-3) scored three touchdowns and converted three 2-point conversions in a 12-minute stretch of the fourth quarter.
Navy's hope for a complete comeback, however, ended when the Mids turned the ball over on downs with 6 seconds to play.
Renfree tied a Duke record when he completed his first 16 passes and completed 17 for 18 passes in the first half for 180 yards. He finished with 28 completions in 30 attempts, setting a Duke record with a 93.3 completion percentage. His backup, Brandon Connette, picked up some big first downs rushing and ran for a score.
During the Devils' six-game skid, Renfree had thrown 15 interceptions, including five in a 28-13 loss to Miani on Oct. 16.
"That's the real quarterback we saw out there today in Sean. He drove us up and down the field," said Duke wide receiver Conner Vernon, who caught a 29-yard touchdown pass from Renfree that put the Devils ahead 31-7 with 1:02 left in the third quarter.
"It feels good to get any win, especially after the last few weeks when I have struggled," Renfree said. "It feels great to get in a groove offensively and score some points again."
Dobbs completed 13 of 27 passes for a career-high 227 yards and two TD passes. He also rushed for 83 yards in 22 carries and added a 2-point conversion. Dobbs is now Navy's career scoring leader with 266 points and all-time touchdowns rushing leader with 44.
Navy was coming off a big win over Notre Dame last week and came into the Duke game looking for a win that would assure the Midshipmen of their eighth straight bowl appearance.
"We have to be ready to play each week and clearly we did not today," Navy defensive back Wyatt Middleton said. "No matter the opponent or the stadium, you are playing and you have to approach each game the same way."
Navy had won three games in a row since starting the season 2-2.
"I did a bad job of getting us ready to play. ... We played bad and I coached a bad game," Navy coach Ken Niumatalolo said. "We missed assignments, eyes in the wrong place, checks on offense that I didn't know where they came from. We were in a daze at the start. We played horrible, but battled back."
The 24-point deficit for Navy was its biggest at halftime since the Mids trailed 31-0 to Connecticut in a 2002 game.
"With the start we had we didn't deserve to win," Niumatalolo said.
Duke's first-half scoring drives covered 68, 76, 45 and 64 yards.
In the first half, Duke outgained Navy 268 yards to 67 and held the ball for almost 19 minutes.
"This is the most resilient group of young men I've ever been around," Duke coach David Cutcliffe said. "We won by doing what we had to do to win in the fourth quarter. When you are 1-6 and things start getting away from you, it is very difficult to grasp hold of the momentum again."