Thiem is now 4-0 overall against Cilic in career meetings, including a third-round win at the US Open earlier this month.
"I didn't want to lose too much tension after my victory in New York and I'm really how I did it, really happy with my first round. I was facing another great champion today, so the transition to the clay and to the cold conditions worked out really well," said Thiem, who didn't play any matches on clay between the US Open and Roland-Garros.
"I love the conditions because I'm from Austria, so I know how it is to play in these cold conditions. Back in juniors and when I started to play Futures, it was always like that, 10, 15 degrees cold, so I love it when it's not too fast, so I can be a little bit behind the baseline, make a lot of returns in court. I feel well and I felt well from the first moment I came here again this year, so I'm looking forward to an exciting second round."
Thiem's next opponent is American qualifier Jack Sock, who beat his countryman Reilly Opelka 6-4, 6-4, 6-3.