Fantilli, who was selected with the No. 3 pick in the 2023 NHL Draft, beat Darcy Kuemper glove side from the high slot to put Columbus ahead 3-2 at 16:17 of the third period.
Patrik Laine then scored into an empty net with 56 seconds remaining for the 4-2 final.
Laine and Cole Sillinger each had a goal and an assist for the Blue Jackets, who finished the preseason 4-3-1. Elvis Merzlikins made 25 saves.
John Carlson and Alex Ovechkin scored for the Capitals, who went 3-2-1. Kuemper made 21 saves.
Boone Jenner gave the Blue Jackets a 1-0 lead at 4:57 of the second period.
Carlson responded at 6:18 to tie it 1-1.
Ovechkin then scored his first of the preseason at 10:34 to put Washington ahead 2-1. He redirected in a backdoor pass from Lucas Johansen.
Sillinger tied it 2-2 at 6:29 of the third period.
