Ramkumar survived some anxious moments before humbling Elgin, who is a top-100 player in doubles, 6-3 7-5.
Ramkumar will now fight it out with Slovakia's Norbert Gombos, who came from behind to shcok third seed Serbian Dusan Lajovic 2-6 6-1 6-4.
On another outside court, India's Sanam Singh, ranked 391, had a poor outing as he crashed out after suffering a 5-7 5-7 defeat against Frenchman Federik Nielsen, who is ranked 618.
With the main draw matches starting tomorrow evening, the final qualifying events would be held tomorrow afternoon. Results of second round qualifying:
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H Laaksonen (SUI) d G Soeda (JPN) 75 64 N Gombos (SVK) d D Lajovic (SRB) 26 61 64 P Oswald (AUT) d R Ram (USA) 61 36 75
I Marchenko (UKR) d A Giannessi (ITA) 63 64 R Albot (MDA) d Z Zhang (CHN) 76(2) 63
R Ramanathan (IND) d M Elgin (RUS) 63 75.