15-year-old Bellis could not deliver the fairytale American tennis fans had hoped for.
Maria Sharapova averted an early exit while China’s Peng Shuai upsetted fourth-seeded Agnieszka Radwanska.
American wild card Bellis took her place alongside five-times US champions by stunning 12th seeded Cibulkova.
Ivanovic beat Alison Riske 6-3, 6-0 in first round while 2004 champ Kuznetsova lost 3-6, 6-2, 7-6 to Erakovic.
A steamy first day at US Open proved more than a little stressful for several favourites on Monday.
But one sporting peak no Canadian has yet to reach is the top of the tennis mountain as a grand slam winner.
wMurray said, players will seek out partners whose styles resemble those of scheduled opponents.
The Serb could meet either Andy Murray or Jo-Wilfried Tsonga in the quarter-finals.
World no. 2 Rafael Nadal has withdrawn from the tournament because an injured right wrist.
A wrist injury forced Nadal to skip the tournament; he also missed Rogers Cup and Cincinnati Open.
Serena finished last U.S. Open tune-up by beating Ana Ivanovic 6-4 6-1 to win her first title at Cincinnati.
Serena beat Wozniacki 2-6, 6-2, 6-4, and second-seeded Federer turned back fifth-seeded Raonic 6-2, 6-3.
The second-seeded Federer defeated Murray 6-3, 7-5 after the Scot had taken a 4-1 lead in the second set.
In a tight contest that did not feature a single break, Williams needed nearly two hours to advance to the last 16.
Third-ranked Federer appeared sluggish at times as he struggled to tame the 46th-ranked Canadian.