Rogers and 25th seed Gavrilova battled for three hours and 33 minutes eclipsing the previous record of 3:23 set in 2015 when Johanna Konta defeated Garbine Muguruza 7-6 6-7 6-2 in a second round clash.
World number 62 Rogers moves into the third round where she will face fourth seed Elina Svitolina.
(Reporting by Steve Keating in New York; Editing by Ian Ransom)
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