Wimbledon champion Elena Rybakina, meanwhile, is discovering that her big serve and heavy groundstrokes can do damage on clay courts, too.
The Kazakhstani was dominating 21-9 with winners when Ukrainian opponent Anhelina Kalinina retired due to a left thigh injury early in the second set of the rain-delayed Italian Open final early on Sunday morning.
Medvedev’s fifth title of a stellar season and 20th overall leaves him as perhaps the outstanding contender for Roland Garros which begins on May 28.
The 27-year-old, who was out of the top 10 in February, is set to climb to No.2 in the world and will take the second seeding behind Carlos Alcaraz in Paris, with Novak Djokovic dropping down to three.
Medvedev drew first blood on Sunday in the first Rome final since 2004 not to feature 22-times grand slam champions Rafael Nadal or Djokovic.
He broke in the 12th game where he met a feeble drop shot from Rune with a powerful drive to wrap up the first set.
Rune, at 20 the youngest finalist at the Foro Italico since Spaniard Nadal 17 years ago, broke to love in the first game of the second set and pounced again for a 4-3 lead after Medvedev hit back to level the scores.
But the aggressive world No.7 appeared to run out of steam late in a physically demanding spell to hand the advantage back to Medvedev, who produced a tight hold thanks to two huge serves before closing out the victory in style.
“I always want to believe in myself and I always try to do my best as I want to win the biggest tournaments in the world,” Medvedev, who had not won a match in Rome before this year’s tournament, said.
“At the same time, honestly I didn’t believe much I can win a Masters 1000 on clay in my career because usually I hated it and I didn’t feel good on it, nothing was working.
“Before this tournament already in Madrid and Monte Carlo I was not feeling too bad. I didn’t have any big tantrums and was like ‘OK, let’s continue’ and here I felt amazing in practice.
“But then you need to play the toughest opponents in the world and try to make it. I’m really happy that I managed to do it and prove to myself and everybody that I’m capable.”
Rybakina's title triumph, meanwhile, was a timely boost ahead of the year’s second grand slam, the French Open, on clay at Roland Garros starting next weekend.
“I can play good on all the surfaces,” Rybakina said.
“It’s just maybe for clay I need to be ready more physically and maybe have a lot of preparation.”
It’s been quite a year for Rybakina, who reached the final of the Australian Open, also won an elite title in Indian Wells and was the runner-up in Miami.
“I’m proud that I can maintain this level,” she said.
“I can see improvements on the court, physically also. ... I think there is still a lot of room to improve.”
On Monday, Rybakina will move up to a career-high No. 4 in the rankings and will be a leading contender at the French Open.
“She’s serving 200 kph. She’s also making winners like no one on tour,” Kalinina said.
“Anyone can win in Paris, but she has good chances.
“I am sure if she’s going to do like this, maybe new world No.1 for sure.”
Rybakina was leading 6-4 1-0 15-0 when Kalinina called for a trainer and grasped her left leg as she teared up. She then decided she couldn’t continue.
The final began at almost 11pm on Saturday and Rybakina lifted the trophy after midnight on Sunday.
Rybakina earned her biggest title on clay. Her only other trophy on the surface came in Bucharest in 2019.
The 47th-ranked Kalinina was playing in the biggest final of her career, and has been dedicating her performances to her war-torn country.
Kalinina’s family home was destroyed in a Russian attack last year.
Also, her elderly grandparents have had to relocate from the southern city of Nova Kakhovka - which is held by Russian forces - to Kyiv.
Kalinina’s parents work as tennis coaches in Kyiv and she said on Friday there was a “huge, huge bomb near them, near their academy” a few days ago.
Kalinina spent more than four hours longer on court than Rybakina entering the final, having won the longest match on the women’s circuit this season - three hours, 41 minutes against Beatriz Haddad Maia in the quarter-finals.
“I feel like I am at my physical limit today,” Kalinina said.
Top-ranked Iga Swiatek also retired in the third set against Rybakina in the quarter-finals due to a right thigh injury.
AAP