Alcaraz had won the tournament in 2022 and 2023 but the top seed seemed to be struggling with an injury midway through the match, allowing Rune to capitalise and win his first trophy since the Bavarian Open in April 2023.
But Sunday's title was well deserved for Rune, who had also beaten second seed Casper Ruud in the quarter-finals, while Alcaraz dropped to third in the ATP rankings, below Alexander Zverev who won the Munich Open earlier on Sunday.
"It means the world, it was such a great match. In the beginning I was a bit stressed because Carlos obviously played big-time tennis and I had to breathe a lot and find my rhythm," Rune said.
Alcaraz was out of the blocks early in the opening set and he put on a show with his powerful baseline returns and the occasional drop shot that had Rune scrambling as the Spaniard broke to go 3-2 up.
But in a span of a few minutes, Rune broke right back to go level before going up 4-3 to stun the fans watching on at Spain's oldest tennis club. Alcaraz then found himself serving to stay in the set twice before forcing a tiebreak.
Alcaraz saved two more set points in the tiebreak as Rune began to dictate points once again and the Dane finally converted his fifth set point when the top seed's return went long.
"When he broke me, I think I got more into the match and I played more of my tennis. It was a big battle in the first set," Rune added.
"I know how it feels to lose this kind of first set, it was super important to win it and gain the momentum. So I'm so proud of myself."
Alcaraz took a 2-1 lead in the second set before he took a medical timeout to deal with what seemed like an issue with his thigh muscle or groin. He did not fare any better on his return as Rune elevated his game.
The Dane was very effective at the net, winning 12 of 16 points, while Alcaraz's unforced error count began to climb as the home fans groaned in frustration when Rune went 5-2 up.
Rune eventually served to love as Alcaraz's return hit the net on championship point to give Rune the title.
The Dane then revealed he had taken notes from how Novak Djokovic beat Alcaraz in the Olympic final at Roland Garros.
"I thought to myself, 'OK, let's try to play that kind of style,' really make him play a lot of balls," Rune said.
"I'm very happy with how I stayed composed when it really mattered. I was also very brave when it mattered."Â
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