The talented Chennai lad, who ousted India No. 1 Somdev Devvarman yesterday, faced a strong challenge from Miki Jankovic of Serbia before the Indian wrapped it up 6-1 5-7 7-5 in a battle between two 20-year-olds that lasted two hours 12 minutes.
The Tamil Nadu youngster remained the only Indian in the fray in the last eight, as earlier on the same court Bhambri, who was runner-up in the last week's USD 100,000 Delhi Open ATP Challenger, went down to sixth seed Radu Albot of Moldova 6-3 2-6 6-1.
The highlight of the day was German qualifier Richard Becker, who came back from behind to stun eighth seed and 166th ranked Kimmer Coppejans of Belgium 4-6 6-3 6-3 in one hour 56 minutes.
Ranked 425 Becker will be up against third seed Ruben Bemelmans, who is ranked 139.
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Meanwhile, seventh seed Australian Alex Bolt pulled out after sustaining injury in his left-hand elbow as Egor Gerasimov of Belarus got a walkover and will now face top seed Australia's James Duckworth in the quarters.
Fresh from his inspiring win over Devvarman yesterday, Ramkumar took the first set lead when he won five games in a row, breaking Jankovic twice in the second and fourth game as the Serb could hold his service only once in the sixth game.
Jankovic fought back in the second set, which went neck-and-neck as both the players held their respective serves till the Serb broke Ramkumar in the 12th game to take the match into the deciding third set.
Down 4-5 after he failed to retain his serve in the eighth game, Ramkumar managed to turn it around and fired three aces to hold the serve in the 10th game.