In earning his first PGA Tour victory at the age of 23, Smith became the third youngest Australian victor on the PGA Tour since 1970 when comprehensive records began.
The Kevin Kisner-Scott Brown and Nick Watney-Charley Hoffman teams were tied for second.
"We knew we had to have it", said Kisner of his eagle. "Hopefully I've showed enough this week and will continue to play well to get on the team", said Smith.
With the chance to win it for his team Blixt pushed his birdie putt, sending the combatants back to the familiar 18 tee once again.
Smith and Blixt led by one shot entering the final hole of Sunday's rain-delayed fourth round.
"It's awesome isn't it", whispered Blixt before hugging the 23-year-old Australian around the neck.
Jordan Spieth and Ryan Palmer combined to birdie seven of nine holes in the middle of their round to pull as close as three strokes back with three holes to play, but couldn't quite overcome a deficit that had been as large as six strokes. Both players earn 2-year TOUR exemptions and other perks and were making their first playoff appearances.
Bucks overwhelm Raptors 104-77, take 2-1 series lead
The moves didn't stop there for the Bucks, as their mascot showed off some comedy to diss the Raptors in Game 4, as well. This first round matchup was back-and-forth as the Raptors would barely pull through and win the series in seven games.
Blixt and Smith looked to have the first official team event on the PGA Tour in 36 years sewn up on Sunday before a remarkable finish saw the long-time leaders caught at the last.
The 28-year-old Smith had finished sixth at the Valero Texas Open last week and previously finished 10th at the Shriners Hospitals for Children Open this season.
Kisner, Brown, and Blixt all put their shots on the green and then Cameron Smith stuck his at around two feet leaving himself with a makeable birdie opportunity.
"To have a putt to win on the PGA Tour when you've been working toward it your whole life is a completely different feeling", Smith added. The PLAYERS Championship begins on May 12 at TPC Sawgrass. It featured two-man teams playing two better ball rounds and two alternate shot rounds.
Fourballs: Each player has their own ball, and the team's lowest score on each hole counts. Smith and Blixt could have won it on earlier playoff holes but missed short birdie putts.
Kelly Kraft and Kevin Tway shot an 11-under 61 to vault into third, four strokes adrift of the leaders. The playoff will be in the same format as the final round.