Dobbs and Vince Murray each ran for two touchdowns, Joe Buckley kicked a 24-yard, game-winning field goal in overtime and Navy won its fourth straight, beating SMU 38-35 Saturday night.
The Midshipmen (5-2) were held to 11 yards in the second quarter as they fell behind 21-7 in front of former President George W. Bush, who handled the honorary coin toss before the game.
Behind Dobbs and its powerful ground game, Navy scored on four straight possessions and rushed for 247 yards after halftime.
"It was definitely an emotional roller coaster," Dobbs said. "We only need to have a mustard seed. It's real small but real strong. We felt the whole game they couldn't stop us. We stopped ourselves."
SMU (3-3) forced overtime on Bo Levi Mitchell's 10-yard touchdown pass to Aldrick Robinson with 1:35 left.
The Mustangs had the ball first in overtime and lost a yard on three plays before Matt Szymanski missed a 43-yard field goal.
Dobbs carried twice to give Navy a first down on its possession. Then the Midshipmen ran three plays up the middle to center the ball for Buckley, who also hit a 38-yarder to beat Air Force on Oct. 3.
"This was like a heavyweight battle," Navy coach Ken Niumatalolo said. "There are some hits you take, like an uppercut, and you hit back with a jab."
Murray rushed for 141 yards and Dobbs added 89 on the ground as Navy won its fifth straight overtime game. Dobbs, who came into the game leading the nation in scoring, has 16 touchdowns this season.
After halftime, Murray gained 101 yards on 15 carries.
"It wasn't anything I did," Murray said. "I just tried to hit the hole hard. The line played awesome tonight and opened holes."
Shawnbrey McNeal rushed for 131 yards, Zach Line scored twice and Sterling Moore returned a fumble for a touchdown as the Mustangs fell to 1-10 all-time in overtime.
Emmanuel Sanders became SMU's all-time leading receiver on a 6-yard catch early in the third quarter. It was his 236th career reception.
"We played good enough to win defensively," Mustangs coach June Jones said. "If you had told me we could have made them punt five times, I would have thought we'd won."
After going three and out on its first drive of the second half, Navy's offense got on track.
Dobbs connected with Greg Jones for 39 yards and then hit Mario Washington for a gain of 13. Three plays later, Murray's 3-yard TD run that brought the Midshipmen within 21-14.
Dobbs, who came in leading the nation in scoring, added a 13-yard run to tie the game at 21 with 4:17 remaining in the third. The junior quarterback has scored in all eight of his career starts.
After SMU grabbed the lead back on its next drive, Murray broke loose for a 52-yard gain and scored two plays later.
Dobbs gave Navy a 35-28 advantage on a 5-yard run with 9:11 left.
Navy was the first FBS team in the 11 years not to throw a pass in a game when it beat SMU in 2008. The Midshipmen piled up 404 yards on the ground on 77 attempts in their 34-7 victory.
The Midshipmen rushed the ball six straight times the first time they had the ball, capped by Marcus Curry's 31-yard touchdown run.
SMU answered on its next possession, tying the game on Line's 3-yard run.
The Mustangs scored twice in a 16-second span to take a two-touchdown lead.
Line's 6-yard run gave the Mustangs a 14-7 lead with 8:39 left in the first half.
On Navy's first play from scrimmage on its next drive, SMU linebacker Pete Fleps forced Dobbs to fumble and Moore picked up the loose ball and stepped into the end zone for a 1-yard return with 8:23 remaining before halftime.
"We came out on fire and then started hurting ourselves," Dobbs said. "I felt like my world came down on me after the fumble."
Bush also handled the pregame coin toss for the first regular-season game at the new Dallas Cowboys stadium on Sept. 20. The visiting New York Giants kicked a field goal on the final play to win that one too.