The Czech edged out the four-time Grand Slam champion in a closely fought first-set tiebreak after neither player was able to break their opponent's serve.
Spain's Alcaraz appeared to be struggling at the beginning of the second set but broke in the sixth game to level.
However, Machac powered back and broke Alcaraz again in the 11th game to claim the shock victory.
"Against him, I have no other options, I have to play this well to beat him," 23-year-old Machac said.
Machac will now face world number one Jannik Sinner in the semi-finals.
