The 22-year-old 13th seed, already leading the charts for claycourt wins this year, was cool, calm and composed as he recovered from the loss of the opening set to make it three wins in four weeks against the German.
Thiem now has his eyes on a deep run with Spain's unseeded Marcel Granollers waiting in the last 16 rather than nine-times champion and fourth seed Rafael Nadal who withdrew on Friday because of a wrist injury.
Zverev, 19, showed just why he is being tipped to lead the new generation of players when he took a high-quality first set.
Thiem took charge thereafter, however.
Having levelled the match he broke in the third game of the third set. Zverev recovered and had two break points to get back to 4-4 but he could not take either and Thiem moved 5-3 ahead with a glorious single-handed backhand winner.
Zverev, whose zebra-design shirt was covered in red dust after a fall, dropped serve to love to hand Thiem the third set and was rattled throughout the fourth as the match slipped away.
"We've played three times in four weeks and the other two went to three sets and now this went to four, so I knew it was going to be tough," Thiem, like Zverev a former junior finalist here, said on Court Suzanne Lenglen.
"This was my first match on a big court at Roland Garros and it was a great experience."
(Reporting by Martyn Herman; editing by Clare Fallon)
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