Bhambri, who is in good nick, routed the world number 183 6-0 6-2 in the second round of the men's singles qualifiers.
The 25-year-old Indian, ranked 122, won 54 points in the 57-minute contest, breaking his rival six times in the match.
Bhambri will now fight it out with Canadian Peter Polanksy for a place in the main draw.
If Bhambri clears the final hurdle, it will be his third appearance in the Australian men singles main draw.
Ramkumar Ramanathan, India's next best singles player in the rankings at number 139, will play his second round later in the day.
The 23-year-old from Chennai is up against French man Gleb Sakharov, ranked 156.
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