Victory for the seven-time Grand Slam winner extended his unbeaten run at ATP 500-level events this season to 15 matches.
For the defeated Medvedev, it was nonetheless a fruitful week as his fifth consecutive run to at least the last four of a tournament secured the former world number one his spot in the season-ending ATP Finals next month.
"It's a great feeling, beating someone like Daniil on an indoor court, after the (run) he was having," Alcaraz said.
"I'm really happy to have the chance to play another final, and my first one here in Vienna."
Alcaraz edged in front in the fourth game of the first set as he broke the Russian, but Medvedev riposted in the very next game to get the opener back on serve.
And it stayed that way until a double-fault off the 30-year-old's racquet presented Alcaraz with two set points at 5-4, the first of which he duly converted.
Alcaraz looked to be on the brink of his fifth final of the year when Medvedev dumped a volley into the net, allowing the Spaniard to get 4-2 ahead.
Again, the world number five refused to let his head drop, and hit straight back on the Spaniard's next service game with a break to love.
In the tie-break, both players initially struggled behind their own serve before Alcaraz won five consecutive points to seal his berth in Sunday's showpiece match.
De Minaur earned one of the biggest wins of his career, defeating world number one elect Zverev 6-4, 1-6, 7-6(4) to reach the Vienna final for the first time.
The Australian improved to 10-0 indoors this season, kept alive his hopes of qualifying for next month's ATP Finals and advanced to the 23rd tour-level final of his career.
De Minaur halted Zverev's winning run and denied the German a place in the final days after it was confirmed he would move top of the world rankings on Monday.