The 46-year-old is a twice winner on the U.S. PGA Tour but started the final day well out of contention at four-over and opened his round inauspiciously with a bogey at the first.
The Australian got the shot back at the second, however, and picked up a further four strokes to reach the turn at level par for the tournament.
Four more birdies to the 17th sent him soaring up the leaderboard and when he snaked his putt across the 18th green and into the hole, he was second only to overnight leader Matt Jones.
He had also bettered the sizzling 63 that world number one Jordan Spieth shot to win the title on the new layout at the Australian Golf Club last year.
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"I felt nice and relaxed out there," he told reporters. "The hitting was fantastic and it just gave me the opportunity to make the putts.
"I was just seeing them really well and obviously it's a bonus to get that one on the last. I was more looking at trying to give it a chance but make sure I was a chance to still make the birdie.
"I ran a golf course, I thought Jordan's round last year, eight (under), was pretty impressive and just to shoot the 61, yep, very happy."
Pampling thought a few glasses of his favourite tipple, Bundaberg rum, in the company of his former and current caddies on Saturday had helped fire him up for the lowest round of his career.
"I had a couple of Bundies," he said. "It was nothing major, just a couple of nice social drinks.
"I normally don't drink during the tournament but ... at four over you really didn't think much was going on.
"So, yeah, I guess it fuelled up the tank and I came out on fire."
A total of six-under for the tournament might not earn Pampling a first Australian Open title but it will almost certainly secure him a spot at next year's British Open.
The top three players at this week's 100th Australian Open not already qualified will tee off at Royal Troon next July, a prospect that delighted Pampling.
"It's just a nice little cherry to have at the end," he said.
"Obviously, you want to hold the trophy up but it's certainly awesome to be getting back into the British again."
(Editing by Greg Stutchbury)
