(CNN) -- When Matt Jones missed a six-foot putt last year, it cost him a coveted place at the Masters.
The Australian golfer made up for it on Sunday, clinching the last spot in the field for Augusta next week after snatching his first PGA Tour victory in 156 starts at the Houston Open.
While his lip-out at the BMW Championship in August denied him a spot at the Tour Championship, which guarantees entry to the following year's opening major, this time the 33-year-old made sure in dramatic style.
He drained a 46-foot birdie putt to force a playoff with longtime leader Matt Kuchar, and then sunk a 42-yard chip on the first extra hole while the American could not match it from the greenside bunker.
Jones will make his Masters debut alongside fellow Australian Steven Bowditch, who last week clinched entry when he caught Kuchar with nine holes to play at the Texas Open and also went on to win his first PGA Tour title.
That makes four winners from the southern hemisphere continent this year, with Jason Day having won the World Match Play Championship in February and John Senden the Valspar Championship last month.
Compatriot Adam Scott, who will be defending his Masters crown, was third at the Arnold Palmer Invitational the week after Senden's win after blowing a big lead on the final day.
Jones shot 66 while Kuchar -- who blew a four-stroke overnight lead -- carded 72 as both finished on 15-under 273.
Spain's Sergio Garcia was two shots back after a 70, with Cameron Tringale fourth ahead of fellow Americans Shawn Stefani and Rickie Fowler.
Former world No. 1 Rory McIlroy showed form ahead of Augusta with a seven-under-par 65 that left him tied for seventh in a group including fellow two-time major winner Retief Goosen of South Africa, who closed with 70.
"I wanted to shoot something in the 60s at least today to give me some positive vibes going into Augusta," McIlroy said.
"I couldn't be in a better mood getting on the plane and heading over (to Augusta) tonight."
American veteran Phil Mickelson confirmed his fitness ahead of his bid for a fourth Green Jacket at Augusta as he finished tied for 12th after a final-round 71, alongside former world No. 1 Lee Westwood and 2003 British Open champion Ben Curtis.
"I'm a little nervous heading into next week," said Mickelson, yet to win in 2014 and battling injury setbacks.
"I haven't had the results, I haven't been in contention, I haven't won this year, so I'm certainly nervous about my chances, but it's my favorite week of the year."
South Africa's Charl Schwartzel, the 2011 Masters winner, was tied for 19th.