All three players missed the fairway with their drives on the first playoff hole, the tricky par-four 18th, but only Holman found the green with his approach.
The 24-year-old safely made a par to claim the title after Varner and Frittelli both made bogeys at the Royal Pines Resort on Australia's Gold Coast.
Holman had been two shots clear at two-under with two holes to play but bogeyed both, settling for a final round of 73 after opening the door for Varner and Frittelli.
Playing together in the last pairing, neither man was able to birdie either of the last two holes, with both signing for 75s and joining Holman in the playoff.
South Africa's Zander Lombard, who had shared the overnight lead with Varner and Frittelli, finished one stroke out of the playoff at one-over while Australia's Cameron Smith dropped three shots in his last six holes to finish at two-over.
By winning the tournament, co-sanctioned by the European Tour, Holman ensured he won the Australasian Order of Merit, which earned him a place in next year's British Open at Royal Troon and the World Golf Championships Events.
It also earned him a European Tour card for the next two seasons.
"It's huge. I didn't realise what was on the line," Holman told reporters. "It's probably a good thing, to be honest.
"I did think I'd get to those events in the future. I didn't think it would be this quickly.
"To do it off the back of a victory is probably going to be better -- I've deserved it. It's stuff you dream of playing golf as a kid."
(Writing by Julian Linden in Singapore; editing by Sudipto Ganguly)
