The 21-year-old got out of trouble repeatedly with his serve, which produced 22 aces. He had 12 Tuesday night when he opened with a victory over Rogers Cup finalist Richard Gasquet.
Raonic improved to 2-0 over the recently married Baghdatis after beating the Cypriot last October at an indoor tournament in Stockholm, Sweden.
Raonic, from Thornhill, Ont., hit 46 winners, and broke Baghdatis for a 5-4 lead in the final set. But he had trouble finishing out the win, and had to save three break points in the next game. He finally got an opening as he earned a match point and finished the job on a Baghdatis error.
Baghdatis was treated for a back and hip problem in the second set, but didn't seem to affect his play.
Raonic saved all six of the break points he faced and he profited from 33 Baghdatis errors.
Raonic, ranked a career-high 19th in the world, next faces Tomas Berdych of the Czech Republic, a regular in the ATP top 10. The two have never played each other before.
Raonic, winner of three career titles, improved to 32-13 on the season.Suggest a correction