The Swiss player earned his 12th tour-level victory of the year by making wide cuts at the ball from both wings, hitting 26 winners while avoiding one break point.
After an hour and 14 minutes, the 26-year-old, who won his first ATP Masters 1000 trophy in Cincinnati last year, earned a service break in his second return game.
Alejandro Davidovich Fokina vs Borna Coric will take place in the round of 16 of the 2023 WTA Madrid Open on May 1.
Thiem struggled at the start of 2023, with his first-round loss in Miami last month marking his ninth loss in ten matches.
Aslan Karatsev and Laslo Djere will take on each other in the first round of the 2023 Madrid Open on April 27.
Dusan Lajovic and Jason Kubler will take on each other in the first round of the 2023 WTA Madrid Open on April 27.
Marton Fucsovics vs Marco Cecchinato will take on each other in the first round of the 2023 WTA Madrid Open on April 27.
To earn his eighth Top 10 victory, he struck the ball hard to turn Rublev around and remained composed in the third set.
Carlos Alcaraz, the reigning champion, will be the overwhelming favourite to win in Madrid and will try to become just the second person to successfully defend his title.
Alcaraz defeated World No. 5 Tsitsipas in 79 minutes despite dropping serve in the third game of the match.