Australia’s Jason Day has claimed the biggest victory of his golf career, winning the World Golf Championships Match Play Championship.

The 26-year-old Queenslander overcame a brilliant fightback from gritty Frenchman Victor Dubuisson to win with a birdie at the 23rd hole in a thrilling final at the Dove Mountain course in Arizona on Sunday.

Day’s victory in the elite WGC series event earns him $US1.53 million ($A1.70 million) in prize money and a three-year exemption on the US PGA Tour.

It is also expected to catapult him from No.11 to No.4 in the world rankings, behind only No.1 Tiger Woods, No.2 Adam Scott and No.3 Henrik Stenson.

Day was three up through 12 holes in the final but world No.30 Dubuisson rallied to send the match to extra holes and then made two stunning recovery shots from rocky, desert lies on the 19th and 20th holes before finally succumbing on the 23rd when Day holed his four-foot birdie putt.

Day’s only previous win on the US PGA Tour was in the 2010 Byron Nelson Championship.

And he’s endured a frustrating run of near-misses in big tournaments, including runner-up results in three major championships – the 2011 Masters, 2011 US Open and 2013 US Open.

Day earlier eliminated American Ricky Fowler 3-up in their semi-final while Dubuisson beat Ernie Els in the other semi-final.