The midfielder's 13th-minute opener helped the visitors snatch a point in the matchday one fixture.
Having received a pass from Jonathan Lewis, Ofori unleashed a low shot from about 25 yards into the net to put The Bronx Blues 1-0 up.
Alexander Ring added a second goal after the Black Star's effort but two second-half strikes from Christopher Mueller and Tesho Akindele ended the game on a 2-2 score.
The result earned each team a point heading into matchday two.
Ofori rejoined New York City FC in December following an initial loan stint from German side VfB Stuttgart.
Last season, the 23-year-old made 28 appearances involving 21 starts and scored one goal.