Nadal, bidding to reach the semi-finals of a Masters event for the 75th time, followed world No.1 Novak Djokovic – beaten in the third round – out of the tournament.
"For Rafa, it must be incredibly difficult to play with this pressure of always having to win," Rublev who also made the Miami Masters semi-finals at the start of April, said.
"I'm shocked to see the level which he can reach despite this pressure. It's much easier to play when you have nothing to lose."
It was only the second time in 16 appearances in Monte Carlo that Nadal had failed to make the semi-finals.
World No.8 Rublev will face unseeded Casper Ruud, who put out defending champion Fabio Fognini, for a place in the final.
The other semi-final will feature Greek Stefanos Tsitsipas, the No.4 seed, against Britain's Dan Evans, the man who shocked Djokovic in the third round.
Tsitsipas is the highest seed left after world No.2 Daniil Medvedev was forced to withdraw because of a positive COVID-19 test.
Evans followed up his superb victory over Djokovic with a slender win over David Goffin to reach his first Masters 1000 semi-final.
World No.33 Evans, who had come into the tournament having lost his previous 10 matches on clay, overcame Goffin 5-7 6-3 6-4 in two hours and 42 minutes.
Rublev is no stranger to taking out the big names – in 2019, he stunned Roger Federer at Cincinnati in just 62 minutes.
On Saturday (AEST), the 23-year-old won the first set in 38 minutes but Nadal then pocketed the last four games of the 73-minute second set to level the contest.
In the decider, Rublev held his nerve, breaking the Spaniard three times on his way to a famous win.