The 17th-ranked Nishikori defeated Baghdatis for the first time after losing three previous matches.
Nishikori and Raonic will play for the first time in the final, with the Japanese player 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 and used his strong serve and powerful forehand to go up 5-3. He broke 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.
There were no breaks of serve in the second set and went 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.
Murray held to go up 5-4 and then had two match points on Raonic's served in the 10th game of the third set, but could not capitalize as the Canadian held to send it to another tiebreak.
Raonic took control in the tiebreak.
"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," Murray said. "I played better in the second and third sets, but it was a disappointment to not close out the match. It came down to one or two points in the end."
Raonic has won titles twice this year, in Chennai, India, and San Jose, Calif.