Rumford rifled a long iron to four feet at the par-five 18th in the sudden death shootout and he confidently rolled in the putt to seal a fourth European Tour title and first for six years.
"I'm really pleased with the result and I owe a lot to Ronnie my caddy and I've got a great team around me," the world number 253 said in a televised interview after his win.
The Australia had looked set to win the 2,205,000 euro ($2.87 million) event in regulation after six birdies on the front nine helped him to a two-shot lead from Fraser and Whiteford standing on the 17th tee.
But the 36-year-old Australian notched a double-bogey six on the hole after driving into a bush and taking a penalty drop.
That mistake pushed him back to 11-under for the tournament and he needed to roll in an eight foot putt on the 18th to save par after another wayward drive to finish with a four-under-par round of 68 and a 277 total.
Playing partner Fraser matched his 68 and came close to moving into the lead when he narrowly missed a 20ft birdie effort on the last before Rumford's putt.
That left Whiteford (69) in the final group needing to birdie the 543-yard hole to seal a first European Tour title but the Scot produced a nervous chip with his third shot from the edge of the green and then pushed his five-foot putt to win wide of the cup.
Before embarking on the playoff, Rumford called coach Pete Cowan for some advice on how to fix his driving.
"A lot of thanks go to Pete," the Australian said. "I battled with my driver constantly and I guess that's what keeps me out of most golf tournaments.
"I left a few drives right - it wasn't just the last two drives, it was the whole back nine I was feeling stuck and a little bit trapped - had a quick word with Pete and hit a five or six balls off the first tee and it obviously did the trick."
All three found the 18th fairway with their drives in the playoff but Whiteford again went right with his second, while Fraser sent his approach over the back of the green, leaving the flag open for Rumford.
His superb approach pitching short of the flag before rolling up just a couple of feet behind the cup and he kept his composure as Whiteford made birdie and Fraser chipped up close to the flag with his third.
Frenchman Romain Wattel had a final round 69 to finish fourth, two off the playoff, while South African world number seven Louis Oosthuizen (69) was a further shot back.
Past champion Thongchai Jaidee (65) of Thailand was joint sixth alongside Noren and South Korean Kim Hyung-sung (67) in the Asian Tour co-sanctioned event.
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