After starting the final round just one stroke off the lead, Smith's Sunday challenge all but a evaporated with a dispiriting and uncharacteristic three-putt bogey on the very first hole.
Five dreary hours later Smith signed for a lacklustre two-over-par 72 to slump to a share of 17th at 10 under for the championship.
The one-time world No.2 didn't even finish as the leading Australian.
That honour belonged to Marc Leishman, who fired a final-round 67 to finish joint 10th at 12 under, with Lucas Herbert's sizzling 64 vaulting him to equal 17th with Smith.
As Smith collapsed, multiple-major-winning golf titans Jon Rahm and Bryson DeChambeau emerged as third-round leader La Sasso's biggest threats.
At one point, Rahm and DeChambeau looked to be duelling for the title as La Sasso slipped two shots behind.
But the 22-year-old rallied to snare the trophy with a birdie at the par-5 18th in a steely closing round of 65 to prevail at 18 under.
Rahm opened the door for La Sasso with a bogey on his last hole of the day, the par-4 first, in an otherwise dazzling, birdie-filled final-round 63.
"I don't even know what to say," La Sasso said after collecting the $US2 million winner's cheque.
"I thought I played great all day and just waited for my moment and it finally came at the last.
"It's unbelievable. I'm at a loss for words."
Rahm's second place capped off a great year for the Spaniard, who claimed his third straight season points title and his second team crown in a row.
He will now head home to Spain to be with his pregnant wife as they await the birth of their fourth child.
Rahm is under contract to LIV Golf through next season, but may be contemplating a return to the PGA Tour.
In April, it was announced Saudi Arabia's sovereign wealth fund would end its investment in the league after this season.
However, LIV chief Scott O'Neil said last week he was bullish about plans for 2027 and beyond, saying a new chief investor had been lined up.
O'Neil said there was a deadline for players to commit to LIV 2.0, without citing a specific date. He also has not mentioned the size of the proposed investment.
Rahm is among several well-known players who may consider a return to the PGA Tour, along with Smith and DeChambeau, who finished third in Indianapolis.
- with AP
