Raonic provided strong resistance in the opening set, but the big-serving 19-year-old blinked in game nine, producing two double faults as Murray claimed the vital break before holding comfortably to close out 6-4.
Murray, who did not face a single break point during the entire 120-minute match, broke again in game five of set two.
The Scot then continued to serve with supreme authority, keeping his opponent at arm's length and taking the second set by the same scoreline as the first.
Raonic was broken twice more in the third set, as Murray prevailed 6-2. Murray has now reached eight consecutive Grand Slam quarter-finals.