The eight-times champion from Spain applauded his 20-year-old opponent after being tested on court Philippe Chatrier more than the scoreline suggested.
"His ball is so high he was able to hit strong he has completely everything to become a champion," said the world No.1, who for the first time arrived at Roland Garros having lost three matches on his favoured clay this season.
"I think today I played a solid match, I knew that if I didn't I would be in trouble." He briefly was in the third set when Thiem, who stunned world No. 3 Stan Wawrinka in the second round of the Madrid Masters this month, broke and held serve to open a 3-1 lead.
His booming inside-out forehands briefly put Nadal in trouble as the Spaniard eyeballed his opponent.
But Nadal won the remaining games, ending the contest on his second match point when the Austrian sent a forehand long.
Nadal, who next faces Russian Teymuraz Gabashvili or Argentine Leonardo Mayer, is on a quarter-final collision course with last year's runner-up and compatriot David Ferrer, who also wasted little energy reaching the last 32, demolishing Italian Simone Bolelli 6-2 6-3 6-2.
"I am ready for the next round and was very happy with my performance, especially with my consistency," Ferrer, who will be up against Italian Andreas Seppi, said after dismantling Bolelli.
"My season on clay has been good (when asked about beating Nadal on clay this season). I have a good feel."
Seventh seed Andy Murray of Britain, the Wimbledon champion, produced a masterclass to win an entertaining, although one-sided, match 6-3 6-1 6-3 against Marinko Matosevic who was playing in the second round of a grand slam for the first time having previously lost 12 first round matches.
Elsewhere in Paris, Croatian 16th seed Ivo Karlovic reached the third round with a 7-5 6-3 6-4 win over Andreas Haider-Maurer, while American Donald Young knocked out Spanish 26th seed Feliciano Lopez in straight sets.
He will play Spain's Guillermo Garcia-Lopez next after he followed up nicely on his first-round defeat of third seed and Australian Open champion Wawrinka by beating France's Adrian Mannarino 6-4 6-3 4-6 6-0.
Round 2 results:
Leonardo Mayer (Argentina) beat Teymuraz Gabashvili (Russia) 6-2 4-6 6-4 6-4
Guillermo Garcia-Lopez (Spain) beat Adrian Mannarino (France) 6-4 6-3 4-6 6-0
Dusan Lajovic (Serbia) beat Juergen Zopp (Estonia) 6-2 6-4 6-4
1-Rafa Nadal (Spain) beat Dominic Thiem (Austria) 6-2 6-2 6-3
19-Kevin Anderson (South Africa) beat Axel Michon (France) 6-2 6-3 6-2
Donald Young (U.S.) beat 26-Feliciano Lopez (Spain) 6-3 7-6(1) 6-3
5-David Ferrer (Spain) beat Simone Bolelli (Italy) 6-2 6-3 6-2
Ivo Karlovic (Croatia) beat Andreas Haider-Maurer (Austria) 7-5 6-3 6-4
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