The 214-ranked 21-year-old Indian, who made his Davis Cup debut last week in Chandigarh against Korea, rallied to beat his Kiwi opponent 2-6 6-4 7-6(3) in two hours and 22 minutes and booked a last-eight berth in the hard court event.
Ramkumar said it was a relief to win a tie-breaker after losing quite a few in the last few weeks. It was the first tie-breaker that Ramkumar managed to win having lost five in a row since Wimbledon Qualifiers.
Ramkumar took a while to settle on hard courts after playing on grass last week and found his rhythm from the second set onwards.
He then broke Statham, ranked as low as 472, in the third game to create a lead. He served a double fault to face a breakpoint in the fourth but wriggled out with an ace to lead 3-1.
However, the New Zealander broke back in the sixth game to level it 3-3 and eventually it all boiled down to the tie-breaker.
The Indian kept playing aggressively to reach the quarterfinals, where he faces British giantkiller Brydan Klein, who had knocked out top seed Quentin Halys in the opening round.
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