Starting the final round one shot behind Castle Hill Professional, Alex Edge, Burdett posted five birdies on his outward nine to reach 18-under to take a five-stroke lead.
Quietly surging up the leaderboard in the penultimate group, Michael Wright and Chris Wood took advantage of a stumble from Burdett on the back nine to see all players locked on 16-under as they approached the last.
Wright hit a great wedge to five-feet and converted the birdie to finish regulation play with a 17-under tournament total with rounds of 71, 70, 66 and 64.
Burdett, after a great drive, hit a wedge to 15 feet and calmly rolled it in for a final round of 68 and a tournament total of 17-under, taking the tournament to a playoff.
Burdett tapped in for a 5 on the first hole of sudden death to claim the 2019 Vanuatu Open.
“I’ve been playing great lately and this caps of a great few weeks of golf,” said Burdett, who tied for fourth place at the NT PGA Championship the week prior.
“The course was amazing, the weather was great and the people of Port Vila were awesome. I’m stoked to stand here with the trophy.
“A huge thank you to the VGO committee for their tireless work, as well as all the sponsors and volunteers for the week. I look forward to coming back next year.”
Chris Wood took out third place with rounds of 70, 68, 69 and 66 for a 17-under total.
Tim Hart once again continued his strong Ladbrokes Pro-Am Series form, finishing tied for fourth place alongside Blake Proverbs at 14-under.