Murray struggled to deal with the huge serve of the 11th seed, going down 6-4 7-6 (7-3) to slip to his second quarter-final loss in as many weeks.
Murray managed his only break in the 10th game of the second set to stay in the match, but Raonic breezed through the tie-break to seal victory.
Raonic will play David Ferrer in the last four. Spaniard Ferrer came through in three sets against compatriot Feliciano Lopez, 6-7 (4-7) 7-6 (9-7) 6-3.
Murray had been due to play Raonic in the third round of the Miami Masters in March only for the 21-year-old to pull out with an ankle injury. Raonic, the 6ft 5ins (1.95m) right-hander from Ontario, had never beaten a player ranked inside the world’s top eight before but went into his clash with Murray on the back of a straight sets win over sixth seed Nicolas Almagro in the third round. As he rained down serves approaching 150mph on the Scotsman, Raonic won 94% of first serve points in the first set, as Murray could not earn a single opportunity to break. — BBCSport