Rafa Cabrera-Bello of Spain and Frenchman Gregory Havret were eliminated earlier in the playoff.
Zanotti shot a closing seven-under-par 65 to finish with a 19-under total of 269, the same mark as Stenson (67), Cabrera-Bello (67) and Havret (66).
"To be the first player from Paraguay to win on the European Tour is pretty huge," the winner told reporters. "I think in Paraguay everybody is going to be very happy with me.
"I feel very happy. This is a moment I've been waiting for a long time," the 2013 Qualifying School graduate said after picking up the first prize of $452,000.
Zanotti, who was making his 181st appearance on the tour, could now rocket from 305th and into the top 110 of the world rankings.
"When Henrik hit his ball into the water on the fifth extra hole I changed club," he said.
"I was going to hit a driver but I changed and just aimed to the left bunker by the green. Thankfully it worked out perfectly."Britain's James Heath, who carded a 70 for 277, won a new sportscar from the sponsors after recording a hole-in-one at the par-three 16th.
"It looks fantastic," said the 21-year-old. "It's certainly an upgrade from my previous vehicle."
(Writing by Tony Jimenez, editing by Josh Reich)
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