Canadian Raonic slammed down 14 aces on his way to victory over the British world number four to set up a clash with third seed David Ferrer, who saved three match points in a 6-7 7-6 6-3 success against Spanish compatriot Feliciano Lopez.
World number two and holder Nadal, who is chasing a seventh Conde de Godo trophy in eight years, will face another Spaniard in 2010 winner Fernando Verdasco for a place in Sunday's final.
Verdasco went through in the last match of the day after Kei Nishikori of Japan was forced to retire with an abdominal injury when trailing 4-2 in the first set, an ATP spokesman said.
An aggressive Raonic took the initiative from the start against second-seeded Murray and held off a fightback from the Scot at the end of the second set to record one of the best wins of his career as he bids for a third title of the season.
Murray, who failed to get past the second round in his three previous appearances, managed just one break of the mighty Raonic serve, when the 21-year-old Canadian led 5-4 in the second set only to wobble badly when serving for victory.
The tiebreak raced away from the Briton though as 11th seed Raonic forged 6-1 ahead. Murray saved two match points but struck a lame shot into the net as Raonic closed out the match.
"Clay's not (Murray's) best surface, but he consistently does well on it," Raonic said on the ATP website (www.atpworldtour.com).
"Last year he reached the semi-finals at the French Open, Monte Carlo and Rome, so he can play really well on it. For me, it was a big win, regardless of the surface."
Nadal turned in a below-par performance in beating Colombian wildcard Robert Farah on Thursday but on Friday the Spaniard looked much more like the player who is on a 32-match winning streak at his home club in the Catalan capital.
He cracked consecutive aces to seal victory against the eighth-ranked Tipsarevic of Serbia and told Spanish television he was especially pleased with his performance in the first set.
"I think two 6-2 sets against the world number eight is a fantastic result," added the 25-year-old French Open champion.
"Tomorrow I am in the semi-finals and I'll have to play at my best to have a chance so let's see what happens."