The 21-year-old from Thornhill, Ont., will face either Kei Nishikori or Marcos Baghdatis in Sunday's final.
Raonic remains firmly in the chase for one of four remaining spots at the November year-end championships in London and would rise to provisional tenth for the eight-man field should he win the title in Tokyo.
Raonic handed Murray a pair of patch points in the final set with double-faults but salvaged them both before the set went into a tiebreaker.
He earned a winning chance on a Murray lob in the decider, but double-faulted his first winning opportunity of the long afternoon which lasted for nearly two and three-quarter hours.
But Raonic sealed the semi-final on his second opportunity seconds later as Murray sent a forehand wide to lose.
"I came out strong and started the match well," said Raonic, winner of two other titles this season and a loser to Murray when they met just weeks ago in the U.S. Open.
"It was fun to play well, I'm very happy with what I did.
"Andy is one of the toughest players from the baseline and I really had to take my game to him, I was able to play well for most of the time, I hope to do that and more on Sunday."
Raonic ran off with the opening set from the start of play, winning the first six points as he broke Murray to love in the opening game.
The sixth-seed double-faulted for a break point in the sixth game but calmly saved himself to take a 4-2 lead, A love game from Raonic paved the way for a break of Murray to clinch the set in 35 minutes as the Olympic champion sent a backhand out on a miss-hit.
In the second set, Raonic recovered from 0-30 in the opening set to open a 1-0 lead, with Murray staying on serve but cracking a frame in frustration as Raonic asserted his big game for a 3-2 lead.
But the defending champion from Scotland got a grip on his emotions to run the set into a tiebreaker, where Murray levelled the contest at a set each on his first set point as Raonic made a return error.
Murray earned a break for 3-1 in the final set after Raonic saved two previous chances in the game. But the top-seed promptly gave it back as he put a reflex volley into the net for two break points to Raonic and dropped his serve for 4-3 from another unforced error.