Top seed Murray, gearing up for the U.S. Open in nine days, the last grand slam of the year, will face 2014 U.S. Open champion Marin Cilic of Croatia in the final.
Cilic overcame Grigor Dimitrov of Bulgaria 4-6 6-3 7-5, coming back twice from a break down in the third set in a match that ended past 1:30 AM ET (0530 GMT) following a two-hour rain delay after play was stopped in the second game.
Murray has won 11 of 13 matches against 12th seed Cilic.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Heavy rain also fell just before the scheduled start of the Murray-Raonic semi-final and then four points into it there was a delay for several minutes due to some heavy misting.
Raonic seemed off rhythm from the start, double-faulting twice as the Scot registered a break in the opening game.
"He served a couple of doubles that first game and I managed to get the break, and then had the momentum from there," said Murray, who registered his fifth win against Raonic this season.
Two-times Cincinnati winner Murray, playing with energy and excellence from sideline to sideline, broke Raonic again in the ninth game to close out the first set.
The second set went on serve until the eighth game, when Raonic committed another double fault, elected not to volley a lob that fell well within the baseline and netted a forehand on break point, one of his 31 unforced errors.
Murray had a touch of trouble closing out the match as he mis-hit a couple of shots and a light drizzle held up play again for a few minutes before the Briton executed a splendid drop volley to end it on his third match point.
(Reporting by Larry Fine in New York; Editing by Greg Stutchbury/Sudipto Ganguly)
