Raonic, seeded 6th and ranked 15th, will meet Kei Nishikori in Sunday's final after he routed unseeded Marcos Baghdatis of Cyprus 6-2, 6-2 in just over one hour.
Nishikori, ranked 17th, defeated Baghdatis for the first time after having lost three previous matches to the Cypriot.
Nishikori and Raonic will play for the first time in the final, with the Japanese seeking his first title of the season.
Playing under a blazing sun at Ariake Colosseum, the big-hitting Raonic broke Murray in the opening game of the match, then used his strong serve and powerful forehand to go up 5-3, before breaking again to claim the set 6-3.
The Olympic champion looked sluggish from the outset and had to save two break points to hold serve for 1-1 in the second set.
After Raonic held to go up 3-2, a frustrated Murray broke his racket by smashing it on the court.
The were no breaks of serve in the second set, and the contest proceeded to a tiebreak, where Raonic misplayed a volley to give Murray a 6-5 lead and then couldn't handle a Murray forehand that gave him the tiebreak 7-5, squaring the contest.
Murray turned the tide in his favour in the third set by breaking Raonic with a sublime backhand down the line to move ahead 3-1. Murray made it 4-1 on serve and looked to be in control, only to see Raonic break back for 4-3 and then hold for 4-4.
Murray held to go up 5-4 and then had two match points on Raonic's served in the 10th game, but could not capitalize as the Canadian held to send it to another tiebreak.
Raonic took control in the tiebreak and finished it 7-5.
"Live and die by the serve. I'm not afraid to go for it on my second serve. I know what I am capable of," Raonic said.
Murray and Raonic had split their two previous career meetings, both this year. Raonic beat Murray on clay at the Barcelona Open, while Murray knocked Raonic out of the U.S. Open in the fourth round.
"The first set was poor from my side," said Murray. "I played better in the second and third sets, but it was a disappointment not close out the match. It came down to one or two points in the end."
Raonic has won two tournaments this year, triumphing in Chennai, India, and San Jose, California.