He earned nearly $1.2 million for the win, also making amends for a disastrous missed putt last September that appeared destined to keep him from playing at Augusta National.
Destiny, however, had other plans for the 33-year-old who played collegiately at Arizona State.
"Going to Augusta is amazing," Jones said. "The win means everything to me right now because that's what we play for is to win. To have Augusta as a reward for that win is amazing."
In September, Jones lipped out an 8-foot birdie putt on the last hole of the BMW Championship a putt that would have earned him a trip to next week's Masters.
After briefly tying Kuchar in the middle of the round on Sunday, Jones' chances at redemption for last year appeared finished after he bogeyed the next-to-last hole in regulation. The setback left Jones at 14 under, two shots back of Kuchar.
However, Jones in the first of his two memorable moments on the 18th rolled in a 46-foot putt for birdie. That pulled the Australian within one shot of Kuchar, who was watching his closest challenger from the tee.
"I was going to three-putt before I left it short," Jones said. "I didn't care about finishing second or third or fourth; it didn't matter. I was only trying to get the win."
Kuchar went on to bogey the final hole of regulation after sending his second shot into the water. That set the stage for the playoff in the soggy conditions at the Golf Club of Houston.
Jones sent his tee shot on the first hole of the playoff into the right fairway bunker. He then landed just short of the greenside bunker with his second shot, while Kuchar found the bunker from the fairway.Jones didn't leave Kuchar any room for error, sending his chip over the greenside bunker and watching as it rolled in causing a roar from the gallery and leaving Jones standing with his arm raised in celebration.
"I walked up there and told my caddy I was going to chip it in," Jones said. "... You don't know if it's going to lip out, low or high, but when I saw it disappear it's probably the happiest I've been on the golf course."
Kuchar had a chance to match Jones' chip-in, but his bunker shot came up short.
Lexi Thompson closed with a bogey-free 4-under 68 at Mission Hills for a three-stroke victory over Michelle Wie in the Kraft Nabisco Championship.
The 19-year-old Thompson birdied four of the first nine holes to open a five-stroke lead and parred the final nine.
Wie birdied the final hole for a 71.
Thompson finished at 14-under 274 for her first major title.
Matt Jones -15*
Matt Kuchar -15
Sergio Garcia -13
Cameron Tringale -12
Shawn Stefani -10
* - Wins playoff