Alcaraz said he had to “stay strong” and “wait for chances” against Fils before he was able to capitalise on any errors.
“I think his level is high right now and he puts a lot of pressure on his opponents,” Alcaraz said.
“Today I could feel it but in some moments he just made a few mistakes and I tried to make the most of those points.
“I have missed clay. It is good to play the drop shot and it is a shot I use a lot and feel comfortable using. In matches like this I won almost every drop shot I hit and it gives me more confidence.”
Fils made a stunning start to the match as he surged into a 3-0 lead with two early breaks in the opening set.
Alcaraz managed to draw level at 4-4, only for Fils to break once more and then hold serve to take the set as he saved two break points.
Fils squandered seven break points in the second set, and Alcaraz squared the match with a superb lob to break Fils’ serve in the 12th game.
Alcaraz dropped serve once again in the third game of the decider, but managed to break back and then secured another break in the eighth game to the frustration of Fils, who smashed his racket on the clay.
World number 15 Fils failed to regain his composure while Alcaraz kept his cool to seal the match.
Four-time Grand Slam champion Alcaraz is bidding to win his first Masters title since victory at Indian Wells last year.
Later on Friday, Italian Lorenzo Musetti beat Greek defending champion Stefanos Tsitsipas 1-6 6-3 6-4 to progress to his maiden ATP Masters 1000 semi-final.
World number 16 Musetti saved 14 of the 17 break points he came up against and will meet Australian eighth seed Alex de Minaur, who breezed past Grigor Dimitrov 6-0 6-0, in the last eight.
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