Two-time defending champion Alcaraz crashes out in Madrid
Rublev, the world number eight from Russia, came through 4-6, 6-3, 6-2, handing the third-ranked Alcaraz his first defeat on Spanish clay in 25 matches.
Rublev will face either Taylor Fritz of the United States or Argentina's Francisco Cerundolo for a place in the final.
Alcaraz, who was forced to sit out clay court events in Monte Carlo and Barcelona due to a right arm injury, had been in control in the first set.
However, 26-year-old Rublev battled back with Alcaraz looking increasingly weary as the tie progressed in chilly conditions in the Spanish capital and with the roof closed on the Manolo Santana Stadium.
Rublev carved out breaks in the first and fifth games of the decider and celebrated victory when the 20-year-old two-time major winner dumped a tired return into the net.
The Russian clubbed 30 winners as Alcaraz appeared physically spent following his three-set win over Jan-Lennard Struff on Tuesday in a last 16-tie which stretched to almost three hours.