American Mackenzie McDonald,
Classified 211th, As Nadal’s Next Opponent
Thiem took the lead in his match against former world number three Cilic when he broke in the ninth game on his way to sealing the first set.
Cilic, who made 39 unforced errors, became nervous about Thiem’s defense, suffering two more breaks in the second set.
Two poor volleys in the sixth game of the third earned the two-time runner-up the crucial break on the road to victory.
The third-seeded Austrian will play American qualifier, Jack Sock, in the next round.
Thiem, 27, said he was happy to have made a successful transition from playing on hard courts in the New York heat two weeks ago to playing clay in wet 13C conditions in Paris.
“I’m from Austria so I know what it’s like to play in cold conditions,” he added. “When I was in junior I played in 10-degree weather.”