As the scoreline would suggest, it was in the first two sets that Tsitsipas played his most eye-catching tennis, freely coming to the net and keeping Marterer at arm's length throughout.
Highlights - Tsitsipas eases into second round
He started as he intended to continue, breaking his opponent in the first game of the match and doubled his advantage to move 5-2 ahead before serving out the first set to 30.
After missing a chance to repeat the trick in the opening game of the second set, he moved ahead in the third and again broke in the penultimate one and holding his nerve on serve.
Though Marterer rallied in the third set, taking a leaf out of Tsitsipas' book and adopting a more aggressive approach, he failed to craft a single break point chance throughout the match and was comfortably second best in the eventual tiebreaker as the Greek extended his record on clay this year to 13-4.
"Very satisfied. I was playing really well the first two sets of the match. Better than I thought I would. Third set was tricky. I felt like he started pressing more, started going for his shots more, faster, stronger," Tsitsipas said.
"I stayed mentally strong and closed the tie-break at the end.”
Tsitsipas has been touted as a potential challenger for the Roland Garros title, having beaten 11-time champion Rafael Nadal during his final run in Madrid.