World number three Raonic recorded only his second victory over Nadal in eight meetings with a 4-6, 6-3, 6-4 win in the last-eight contest that lasted two hours and 21 minutes.
Defending champion Raonic will now aim to book his place in the final of the tournament for the third straight year when he takes on seventh-seed Grigor Dimitrov in the last-four
In another men's singles clash, third-seed Kei Nishikori also booked his place in the semi-finals of the tournament after easing past Australia's Jordan Thompson 6-1, 6-1.
Nishikori has now set up a last-four clash against second-seed Stan Wawrinka, who survived an early scare from Kyle Edmund of Britain to register a 6-7,6-4, 6-4 win in the quarter-final clash.