Kelly went 17-of-19 for 268 passing yards and rushed for another 81 yards on seven attempts as Arizona State (8-5) claimed its first bowl victory since 2005.
Rashad Ross was Kelly's favorite target, hauling in three of the TD passes while racking up 139 receiving yards on four catches.
Running back Marion Grice finished with 159 yards and two TDs on 14 carries for the Sun Devils, who piled up 648 total yards in the dominating win.
Navy (8-5) was led by Gee Gee Greene, who picked up 112 rushing yards on 12 carries and returned a kickoff 95 yards for a touchdown.
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