Bautista Agut, a beaten finalist in 2013, was in command as usual against Paire, who got to the semifinals without dropping a set.
The second-seeded Spaniard also beat fifth-seeded Paire at the same stage four years ago, and has never lost to him in eight career meetings.
"I played better tennis and aggressive," Bautista Agut said.
He will seek his fifth career title on Sunday.
The unseeded Medvedev outlasted the more experienced Dudi Sela of Israel 4-6, 7-6 (2), 6-2 to make his maiden ATP final.
Sela had match point in the 10th game of the second set, but Medvedev saved it with a winner. He raised his game in the tiebreaker and third set of his first ATP semifinal.