The 29-year old US-born Amritraj, ranked 551, and returning to the tour after a two-year break due to injuries, played sublime tennis to rout Rufin who after a strong start, simply caved in under pressure as his opponent went from strength to strength.
Amritraj, who survived two tough three-setters in the qualifying rounds, will next meet Go Soeda, the eighth seeded Japanese in the second round.
The 22-year old 92nd-ranked Rufin had little left to offer once the former Indian Davis Cupper Amritraj got into his stride with a series of blistering winners and well-angled returns besides strong serves.
Amritraj had every opportunity to wrap up the first set that he began with a break of serve in the very first game, but Rufin broke back in the sixth.
The games went to serve thereafter and in the tie-breaker, Amritraj led 3-0 only to see the Frenchman surge back to take seven of the next eight points to win the set that lasted over an hour.
The flow of the match turned dramatically in the second set that Amritraj took with two breaks of serve in the sixth and eighth to force the decider.
A break of serve in the second game of the third set put Amritraj in command and though Rufin held thereafter, he could not stop the Indian who eventually served out a love game to close the two-hour, 23-minute match.
After a tentative beginning, Amritraj looked the better player as he got into a rhythm while blasting a series of groundstroke winners and also serving exceedingly well.
It was a vintage Amritraj, who was ranked 154 in 2009, thereafter and as the match progressed, the Frenchman faded away, committing errors at crucial stages to bow out of the tournament.
Earlier, Germany's Matthias Bachinger authored the tournament's first major upset when he knocked out seventh-seeded Lu Yen-Hsun 6-4, 3-6, 6-4, to advance to the second round
Left-handed Cedric-Marcel Stebe from Germany, the 22-year old, 177 ranked qualifier, defeated Dutchman Igor Sijsling 6-4, 6-4, to set up a clash with fourth seeded Swiss No.2 Stanislas Wawrinka.
Late Monday night, the Indians Sanam Singh and Vishnu Vardhan gave the experienced players Benoit Paire from France and Stanislas Wawrinka of Switzerland a scare before losing a close opening doubles match 2-6, 7-5, 7-10.
Wawrinka and Paire, seeded fourth and fifth respectively in the singles main draw, took the first set in just 24 minutes, breaking the Indians thrice in the third, fifth and seventh games.
However, Singh and Vardhan, the wild card entries, broke back in the sixth game before their opponents held serve to close the set 6-2.
In the second set, the Indian pair played far better to lead 6-5 when Paire dropped serve with two double-faults giving the home combination the set at 7-5.
The tie-breaker saw the two pairs tied at 7-all before the Swiss-French pair took the next three points to book their entry into the quarterfinals.
The results (prefix denotes seeding):
Singles (1st round): Q-Prakash Amritraj (IND) bt Guillaume Rufin (FRA) 6-7 (4), 6-2, 6-3; Q-Cedric-Marcel Stebe (GER) bt Igor Sijsling (NED) 6-4, 6-4; Matthias Bachinger (GER) bt 7-Lu Yen-Hsun (TPE) 6-4, 3-6, 6-4; Edouard Roger-Vasselin (FRA) bt Andrey Kuznetsov (RUS) 6-3, 6-4.
Doubles (1st round): Benoit Paire (FRA)/Stanislas Wawrinka (SUI) bt WC-Sanam Singh/Vishnu Vardhan (IND) 6-2, 5-7, 10-7.
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