The Irish pulled to within a touchdown in the third quarter when Robert Hughes scored on a one-yard run.
Dobbs and Navy struck back when the Mids quarterback found Greg Jones for a 52-yard scoring pass to go up 21-7.
Early in the final quarter Notre Dame quarterback Jimmy Clausen then found Michael Floyd for a 12-yard scoring strike to pull the Irish back to within a touchdown.
Trailing, 21-14 late in the game, Notre Dame drove deep into Navy territory only to come up empty because of a fumble at the Navy one. Later, Navy a safety scored when Craig Schaefer sacked Clausen in the end zone to put the Mids up, 23-14.
The Irish would not go easy though. Notre Dame recovered an on-side kick after the safety and later pulled to within two of the Mids when Clausen completed a 31-yard pass to Golden Tate.
The Mids recovered a second on-sides kick with 20 seconds remaining to seal the win.
Navy rushed for 358 yards during the game. Notre Dame's Clausen finished with 458 yards passing.
Navy is now 7-3 and bowl eligible for the seventh straight year. The Mids will play in the Texas Bowl. The Mids will next host Delaware on Saturday.
Navy 7 7 7 2 23 Notre Dame 0 0 7 14 21First Quarter
Navy- Ricky Dobbs 1 run (Joe Buckley kick) 7:15
Navy- Vince Murray 25 run (Joe Buckley kick) 14:56
Notre Dame- Robert Hughes 1 run (Nick Tausch kick) 5:03
Navy- Greg Jones 52 pass from Ricky Dobbs (Joe Buckley kick) 3:29
Notre Dame- Michael Floyd 12 pass from Casey Clausen (Nick Tausch kick) 4:46
Navy- Jimmy Clausen sacked Craig Schaefer 1:00
Notre Dame- Golden Tate 31 pass from Jimmy Clausen (Nick Tausch kick) 0:24