It took one hour and 44 minutes for the big-hitting Canadian to wrap up a 6-4 7-6 victory over the world number four.
Murray never really got going during the quarter-final contest, with Raonic dominating on serve with 14 aces.
The world number 25 came out all guns blazing, breaking at 3-3 to eventually serve out for the set.
Murray made more of a contest of it midway through the second set, but Raonic still managed to break to serve for the match.
However, celebrations were put on hold after the Scot broke to force a tie break, in which Raonic prevailed 7-2.