The Italian struggled with Jarry's big serve early in the match and the 22-year-old Chilean, playing in his first ATP final, looked intent on claiming his first tour crown as he stormed through the first set in 21 minutes.
But Fognini adjusted his game and romped through the second set before overpowering a tired-looking opponent to take the title, the sixth of his career.
"He started very well and I had to wait a bit for his serve to calm down," Fognini said. "I've always played well in Sao Paulo and never been able to win so I'm very happy."
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(Reporting by Andrew Downie, editing by Ed Osmond)
