De Minaur began well, breaking the top seed in the third game before taking a 3-1 lead, and breaking again in the seventh after Alcaraz had broken back. But the Spaniard took four of the last five games to claim the set.
The second stanza went with serve apart from the sixth game in which Alcaraz secured the crucial break despite de Minaur twice serving for the game.
The victory gives Alcaraz a 4-0 record against de Minaur who had been bidding for a second successive claycourt semi-final having reached the last four at the Monte Carlo Masters.
However, Alcaraz took the title in Monaco and the world No.2 has now won eight matches on the spin.
"I started quite badly with the serve, I was struggling a little bit mentally with [it]," said Alcaraz. "It was just the first few games with my serve, then I think I improved a lot. I calmed myself down and started to think positively again. Alex started strong, playing aggressively, and the first set was really tight."
Fils progressed after Stefanos Tsitsipas retired in the third game of their quarter-final with the Frenchman 2-0 up.
In the other half of the draw Holger Rune will play Karen Khachanov. Rune beat second-seeded Casper Ruud 6-4 6-2 while Khachanov defeated Alejandro Davidovich Fokina 6-4 7-5.
In Munich top seed Alexander Zverev fought back from one set down to defeat Dutchman Tallon Griekspoor and reach the semi-finals.
The German prevailed 6-7 (6-8) 7-6 (7-3) 6-4 after three hours and 13 minutes.Â
"Finally, I won a close one. I've lost a few of those in the past few months and I always said, 'I need to get one of these.' I did today. I'm extremely happy with how I hung in there," Zverev said.
Zverev will now face Hungary's Fabian Marozsan who beat Belgium's Zizou Bergs 6-3 7-6 (7-4).
American second seed Ben Shelton also advanced to the semi-finals after a 6-4 6-3 win against Luciano Darderi.
Shelton will play Francisco Cerundolo, who defeated David Goffin 6-2 6-4.
with DPA
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