Bopanna and Nielsen won the first round encounter 6-3, 6-7, 6-3 in one hour and 53 minutes at Flushing Meadows here late on Wednesday evening.
They will now take on the US-New Zealand combination of Brian Baker and Marcus Daniell for a place in the pre-quarterfinals.
Baker and Daniell registered an easy 6-3, 6-2 victory over Malek Jaziri of Tunisia and Hans Podlipnik-Castillo of Chile in their opening round clash.
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