Smith, who had earlier missed a birdie putt to win on the opening playoff hole, made no mistake at the second opportunity to seal a win over Kevin Kisner and Scott Brown at the TPC Louisiana in New Orleans.
The Brisbane-born Smith, who earned a PGA Tour exemption through to 2019 with the victory, was lost for words immediately after his triumph.
"I can't even talk," Smith told a television reporter on the green, his eyes brimming with tears.
It was left to partner Blixt to pay tribute to the 23-year-old, who signalled his promise with a fourth-place finish at the 2015 US Open after reaching the event through qualifying.
"I feel like I had the best partner here," Blixt said of Smith.
"He's been playing great all week. He's going to be a superstar one day. I'm very proud of him. Having seen the way he plays golf, the sky's the limit for him," Blixt added.
The play-off had gone to a fourth hole after players on both sides fluffed chances to win on the opening three holes of sudden death.
Kisner and Brown both squandered birdie putts on the 18th to open with a pair of pars, leaving Smith with his first opportunity to roll in a birdie putt for the win.
