Seeded sixth and runner-up last year to Andy Murray, Raonic kept his cool on the crunch points, taking five of eight opportunities to break while the 20-year-old 10th seed converted just three of 18.
The big-serving Canadian sealed the match with his 23rd ace after close to 3-1/2 hours' play.
Raonic will face Roger Federer in Wednesday's quarter-final.
(Reporting by John Stonestreet; Editing by Catherine Evans)
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