At age 20, the Spaniard is the youngest player to reach the Shanghai semi-finals since the tournament's inaugural edition in 2009.
Medvedev, the 2019 Shanghai champion, overcame inconsistent serving to beat Paul 6-3, 1-6, 6-3.
The 30-year-old saved seven break points to hold back the American in a marathon sixth game, giving little away as he broke to take the first set when Paul fired long.
But the 18th-ranked Paul returned inspired in the second set, displaying fantastic defence as Medvedev drove him around the court.
He was rewarded when Medvedev double-faulted twice in a must-win game to tumble into a decider.
The Russian, ranked sixth, cruised to a 2-0 lead in the third set and carried that momentum to the end, breaking again to win on his second match point.
"I think today I was a tiny bit off," Medvedev said afterwards, though he credited his opponent for making it a "tight" battle.
"I managed to regroup," he said. "If I'm playing well, I'm tough to beat."
Earlier, 13th-ranked Jodar beat Norway's Casper Ruud 4-6, 6-4, 6-3 - recovering from a set down for the fourth time in a row this week.
"Casper is a very tough player," Jodar said afterwards. "I had to give my best level today to win this match."
Top seed Alexander Zverev faces Alejandro Davidovich Fokina in the other semi-final on Saturday.