The Spaniard was bidding for his 12th title at one of his favourite venues but had a rare off day as he slipped to a 6-2 4-6 6-2 defeat against sixth seed Rublev.
Russian Rublev is having another impressive season and has now made back-to-back Masters semi-finals after reaching the last four at the Miami Open, but he was given a helping hand by Nadal, who made an unusual number of errors and cut a frustrated figure.
Rublev looked set to win in straight sets but Nadal dug in in typically gritty fashion to restrict his deficit to one break and then won four games in a row to clinch the second set.
But in cool conditions he could not hold off the firepower of Rublev, who swept through the decider.
In the last four, the Russian will face Norway's Casper Ruud, who reached his second Masters semi-final by knocking out defending champion Fabio Fognini 6-4 6-3.
In the last four, Evans will take on fourth seed Stefanos Tsitsipas, who is now the highest-ranked player left in the draw.
The Greek only needed to play one set against Alejandro Davidovich Fokina, taking it 7-5 before the Spaniard, who injured himself in a fall on Thursday, retired in tears.