Schwartzman had defeated 16th ranked Roberto Bautista Agut earlier in the year and pushed Novak Djokovic to five sets at the French Open, but his win over Thiem is his biggest win of the season.
Thiem made eight double faults in the loss.
Earlier, American Sam Querrey overcame a sluggish start to defeat Frenchman Vincent Millot 4-6 7-6(4) 7-5.
The battle was the second meeting between the pair in a week after Querrey defeated Millot in straight sets at the Los Cabos Open on Thursday, a tournament the American won.
The 29-year-old Querrey staved off the upset bid by the 31-year-old Millot despite moving sluggishly around the court and his trusty first serve not being its usual lethal weapon.
His frustration boiled over early in the third set of the ATP 1000 event when he destroyed his racquet after having his service broken. He won the next four games after the outburst.
Querrey will face another Frenchman, Jo-Wilfried Tsonga, the 2014 champion, in the round of 32 on Wednesday.
Emerging Canadian Denis Shapovalov defeated Brazilian Rogerio Dutra da Silva 4-6 7-6(8) 6-4 in a thriller.
Backed by a home crowd that included Canadian NHL Hall of Famer Wayne Gretzky, the 18-year-old staved off four match points in the second set before taking it in a tie breaker.
"The fans really carried me. It was so fun to be out there on the court, it was so loud and energetic," Shapovalov said. "It’s a huge win. It gives me a lot of confidence and a lot of experience."
DEL POTRO NEXT
Shapovalov, who won the junior Wimbledon title last year and was granted a wildcard to the main tournament this year, faces the big-hitting Argentine Juan Martin del Potro in the second round.
Earlier on Tuesday, Czech Tomas Berdych, the number 10 seed, withdrew from the tournament prior to his first round match against Nikoloz Basilashvili citing a rib injury.
"I am sorry I have to apologise all my Montreal fans. I couldn't play, because of my rib dysfunction I need to get well to go to (the) office soon," Berdych said on Twitter.
His withdrawal led to a quick call to the lucky loser American Ernesto Escobedo, who had five minutes to prepare for the match, which he claimed with an upset 7-6(4) 6-4 victory.
In other matches, Belgian David Goffin and Spaniard Pablo Carreno Busta prevailed in their respective three-setters and American Jack Sock beat Pierre-Hugues Herbert in straight sets.
(Reporting by Rory Caroll and Jahmal Corner; Editing by Jeremy Gaunt and Ken Ferris and Amlan Chakraborty)
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