"It means everything," Rune said. "The job is not over yet, but it feels amazing. Playing Daniil is one of the toughest challenges for me on tour.
"I obviously had the right tactics, but it was still so difficult because he puts in great effort and is super solid."
In a rematch of last year's quarter-finals, the 21-year-old Rune showed admirable discipline against Medvedev's vaunted defense, sticking in the rallies and keeping the Russian off balance with a variety of shots while making judicious use of his powerful forehand.
After an early exchange of breaks in the opening set, Rune managed to grind out a key hold for 4-4, saving one break point in a game that went to deuce six times and lasted nearly 11 minutes.
He gained the decisive break for a 6-5 lead and pocketed the set when his rolling backhand drew another error from Medvedev.
The second set was a more straightforward affair after Rune broke Medvedev at love for a 2-1 lead.
After two nervy points as he served for the match, Rune rallied from 0-30 down and punctuated the victory with a forehand winner.
"It's about finding the right tempo, and luckily I’ve got good leg work, so I can reach many balls," Rune said.
"It's about finding the right pace and which shots to hit, because so many players miss too many shots against Daniil.
"He makes you go for more, so I'm super proud that I managed to find the right rhythm."
Rune, whose ascent has slowed since he burst on the scene in 2022 with a victory over Novak Djokovic in the Paris Masters final, reached his first tour-level final since Brisbane in January of 2024.
Draper stuns two-time defending champ Alcaraz
Jack Draper ended Carlos Alcaraz's bid for a rare Indian Wells ATP Masters three-peat on Saturday, toppling the Spaniard to book a title clash with Rune.
Britain's Draper, ranked 14th in the world, held his nerve to beat Alcaraz 6-1, 0-6, 6-4 and reach the first Masters 1000 final of his career.
"This one hurts," admitted Alcaraz, who was trying to join Roger Federer and Novak Djokovic as the only men to win three straight titles in the California desert.
"I don't want to lose any match, but I think this one was even more special to me. It was difficult today, a lot of nerves in the match."
Draper ended Alcaraz's 16-match winning streak in the California desert, leaping out of the gate and wrapping up the first set in 23 minutes as Alcaraz failed to get to grips with the left-hander's serve.
The second set was a mirror image of the first as Alcaraz found his range and after fending off a break point with a 137 mph ace in the opening game broke Draper three times to level the match.
“It was a strange match in all honesty,” Draper said. "Carlos came out a little flat, I sensed that. I had a chance in the first game of the second, and he came up with an ace ...
"What happened to him happened to me, I got tight, I had low energy. I got lost out there for 25 minutes, but in the third, I was really proud of my competitiveness, my attitude and I somehow managed to get over the line."
Draper, who lost a set to love for the first time in his career, broke Alcaraz for a 2-1 lead in the third in a game that featured a lengthy video review that showed the Briton had indeed managed to scoop back a winner off an Alcaraz drop shot without a double bounce.
Upon review umpire Mohamed Lahyani first called for the point to be replayed but then awarded it to Draper, ruling his "not up" call in the rally hadn't hindered Alcaraz.
"Waiting for the ball reviews, they didn't bother me at all," Alcaraz said. "All I can say is Jack came, he played much better than me. That point didn't affect my play at all."
With momentum on his side, Draper broke again for 5-2 lead - Alcaraz failing to put away four game points.
Draper did show some nerves as he served for the match at 5-2 and was broken, abut steadied himself to seal the victory on his second opportunity.