The 25-year old Bhambri overcame a first set lapse to tame Canadian Peter Polansky 1-6 6-3 6-3 in the third and final qualifying round in one hour and 55 minutes.
Meanwhile, Ramkumar had a break chance in the fifth game of the decider but could not convert and eventually lost his third round match 4-6 6-4 4-6 to Canadian Vasek Pospisil.
At Grand Slams, it is Ramkumar's best show, reaching the final qualifying round.
Bhambri, who was junior world number one, had won Australian Open boys singles tile here in 2009 and has played only at this Grand Slam in the main draw since turning Pro.
Asked what makes him perform at Melbourne Park, Bhambri told PTI," I don't know what makes me play better here. Maybe the conditions suit me or I am just familiar with it because I have played here before."
In his first two attempts, Bhambri could not make much of the chance as he drew very strong opponents for his opening matches.
"I am hoping for a better draw of course. I am hoping that I can win a few rounds in the main draw," said Bhambri, who won his sixth ATP Challenger title in Pune in November.
Asked about the first set against the Canadian world number 140, Bhambri said,"It was a nervous start but once I got my rhythm, I started playing more freely.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)