This year's Australian Open finalist fell at the first hurdle in New York - going down 6-1 4-6 6-4 against the American teenager.
Bellis, ranked 1208th in the world, served four aces and won 74 per cent of first serve points to cause the upset of the tournament.
In her first major appearance, Bellis made a flying start as she broke the world number 13 in a flawless first game.
Bellis broke twice more to canter to the first set in 23 minutes.
Cibulkova, who also crashed out in the first round at Flushing Meadows last year, hit back in the second set as she dominated behind her first serve to take the match to a decider.
However, the 12th seed again came unstuck in the final set as Bellis fought back from 3-1 down to book herself a second-round berth with Kazakhstan's Zarina Diyas.