The 26th-ranked Davidovich Fokina fought back to stun wilting top seed Alexander Zverev 5-7, 6-4, 6-3.
In the second semi-final the 20-year-old Jodar beat Medvedev, a decade his senior, 6-3, 6-4 to deny the Russian former world number one a chance to return to the championship match he won in 2019.
Jodar, ranked 13th, started the season ranked 168th. It is his first time in a final at the prestigious 1000 level.
"It was very fun," Jodar told the crowd afterwards, though he credited Medvedev for making the win "tough".
"All the games were very close," Jodar added.
"Super happy with how I handled the important moments," he said, adding that he showed his "best level".
The two players set the tone for a thriller as they pushed the first game to 13 minutes, with Jodar valiantly holding serve.
They traded breaks and battled through gruelling rallies on a humid evening that saw Medvedev, 30, leaning on his racquet and hunched over.
Medvedev, the 2021 US Open champion, saved four set points but Jodar regrouped to win the first set when the Russian returned long.
Jodar needed a medical timeout before the second set but returned to the court technically excellent, racing to a 2-0 lead.
He broke to go up 4-3 when Medvedev double-faulted, and the Russian tumbled to the ground as he tried to save a match point.
Medvedev clung on for one more game to make it 5-4, but Jodar dropped no more points and sent down a decisive forehand to clinch victory.