After losing to Kei Nishikori in his Group B opener on Sunday, the Scot knew defeat in his second match at the O2 Arena in London would see him unable to qualify for the semi-finals.
But, after overcoming a gruelling end-of-season schedule to reach the tournament, Murray produced another battling display to seal his triumph and remain in with a chance of progressing from the round-robin phase ahead of his meeting with Roger Federer on Thursday.
Raonic, who went down to Federer in his first match at the weekend, now faces an uphill task if he is to advance.
The Canadian boasts two strong weapons in his powerful serve and forehand, but both faltered in the opening set.
Murray missed two break-point opportunities in game four, but the respite was brief for Raonic as he sent a forehand long in his next service game to fall 4-2 behind.
Two set points then went begging for Murray at 5-3, but he made no mistake with a third as Raonic could only return a serve into the net.
Murray then took the initiative early in the second set, coming from 40-0 down to reach deuce in game three.
A double fault from Raonic handed him a break point, and the world number eight then sent a forehand wide as Murray moved ahead.
Raonic's response was impressive, however, as a sensational pick-up at the net set up his first break point of the match, which he capitalised on as Murray sent an attempted backhand down the line off target.
An errant backhand from Raonic gave Murray two break points in game 11, and the world number six needed only one as Raonic failed with a half-volley at the net.
Murray wasted one match point, but his victory was sealed when Raonic thumped the ball long to the delight of the partisan crowd.