
Rublev, the runner-up in 2021, came through against his 53rd-ranked rival 7-6 (7/5), 6-3.
Hanfmann had led 5/3 in the tiebreak but was unable to push on and repeat his last-16 win on the Rome clay on the eve of the French Open.
“The important thing was I was able to win against a tough player like Yannick,” said Rublev.
“The last time he beat me and he’s playing better and better. Especially on grass, he’s even tougher to play against because he has such a good serve and a good game at the net.”
Rublev will be playing in his sixth quarterfinal of the season on Friday when he faces Tallon Griekspoor.
Dutchman Griekspoor, who was the champion on grass at ‘s-Hertogenbosch last weekend, defeated defending champion Hubert Hurkacz 6-3, 1-6, 7-6 (10/8).
Hurkacz had beaten Griekspoor in a five-set second round marathon at the French Open recently.
Despite winning 13 titles, Rublev has yet to capture a grasscourt crown.
Jannik Sinner came out on top in an all-Italian clash against Lorenzo Sonego to reach the quarterfinals.
Sinner, ranked at nine in the world, saved all eight break points he faced to clinch a tough 6-7 (4/7), 6-4, 6-4 second-round triumph.
“It was a tough match for sure. He had a lot of chances,” said Sinner after reaching his ninth quarterfinal of the year.
“I made a couple of mistakes in the tie-break but that can happen. On grass courts it’s never easy, and the way I reacted, especially mentally, I guess I did a good job. Obviously playing against him is never easy.”
Sinner will next face Alexander Bublik who reached the quarterfinals with a 6-3, 6-7 (4/7), 6-3 victory against Germany’s Jan-Lennard Struff.
Bublik hit 43 winners, including 23 aces as he reached his second quarterfinal of the season.