With the set level at 4-4, the 26-year-old Portuguese claimed the last two games and will face Raonic in the last eight on Thursday after the Canadian defeated Denis Istomin of Uzbekistan 6-4 6-3.
Raonic, the world number six, fired eight aces and won 25 of his 30 first-serve points as he dominated a match lasting an hour and 25 minutes.
Home favourite Jo-Wilfried Tsonga fought back to secure a 6-7(2) 6-2 6-3 victory over Argentina's Carlos Berlocq.
The second seed, who failed to progress beyond the second-round in Monte Carlo and Madrid, will face Karen Khachanov of Russia in the quarter-finals.
(Reporting by Hardik Vyas in Bengaluru, editing by Ed Osmond)
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