World No. 57 Thiem showed some flashes of genius to break the top ranked Spaniard twice, but was broken seven times and committed 41 unforced errors, reports Xinhua.
The 20-year-old Austrian ran out of steam infront of the invincible eight-time winner who was in ruthless form.
Nadal praised Thiem for his great potential.
"Dominic is a dangerous player and I knew that if I wasn't playing well then I'd be in trouble," said Nadal.
"But he is a future star, 100 percent. His level of ball play is very high. He is strong on the forehand and backhand. He has everything to be a big champion."
Nadal will face either Leonardo Mayer of Argentina or Russia's Teymuraz Gabashvili in the third round.
Fifth seed David Ferrer of Spain also advanced with a 6-2, 6-3, 6-2 win over Italy's Simone Bolelli.