Bodine celebrated in a makeshift Victory Lane after the race was called with 147 of 200 laps completed on the 1-mile track.
Parker Kligerman was second and Kevin Harvick was third. Nelson Piquet Jr. and Cale Gale round out the top five.
Harvick had the dominant truck and led most of the race until the first rain delay. Bodine took the lead shortly after racing resumed and held on for his third straight top-five finish.
Harvick was aiming for his first win at Dover in any series when rain forced a red flag with 80 laps left in the race.
The trucks went back out and Bodine made it to Victory Lane for the first time since 2010.