Raonic, who beat Spain's Nicolas Almagro on Thursday, slammed down 14 aces on his way to victory and a semi-final against either Dave Ferrer or Feliciano Lopez.
Chasing a third title of the year, the 21-year-old took the initiative in the first set, attacking at every opportunity, and held off a Murray fightback at the end of the second set to record one of the best wins of his career.
Murray managed just one break of the mighty Raonic serve, when the 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 Raonic forged 6-1 ahead. Murray saved two match points but struck a lame shot into the net as Raonic closed it out.
Later on Friday top seed Rafa Nadal plays his quarter-final against Serbia's Janko Tipsarevic.