The British No 1 retained his steely determination, despite facing an opponent who was hampered by a foot problem, and completed a 6-4 7-5 win.
After taking the Munich title on Monday, Murray advanced to the latter stages of another tournament to maintain his promising preparations for the French Open.
Raonic limped heavily from the opening game as he failed to retrieve a drop shot, but still managed to hold his serve with a booming ace.
Wincing with pain, Raonic continued to frustrate the Scot with a mixture of powerful serves and ambitious returns.
But a double fault handed Murray his first break point and he opened a 5-4 lead after the Canadian sent his sliced volley wide.
Raonic briefly staved off the Scot, resisting two set points before Murray moved 1-0 up with a fierce forehand at the net.
Murray appeared ready to pounce on his injured foe at the start of second, but Raonic grimly defended a break point to hold for a 3-2 lead.
It was then Murray’s turn to endure discomfort as he held off a string of break points after his hobbling opponent staged a determined stand.
Raonic’s resistance finally wavered at 5-5, gifting another break with an overhit forehand, and Murray served out for a place in the semis.