Nishikori, the runner-up to Novak Djokovic last year, fired 37 winners but Verdasco, aided by persistent swirling winds, used his varying pace and depth to rattle the eventual winner, inducing 48 unforced errors.
Verdasco rallied to force a first-set tie-break after trailing 3-0 but Nishikori's lunging half-volley backhand winner enabled him to take the set.
Nishikori served for the match at 5-4 in the second set but Verdasco saved a match point to break back and eventually forced a decider with a scorching cross-court backhand.
Nishikori won six of seven games in the third set to advance to the Round of 16.
Raonic had been scheduled to play American qualifier Jared Donaldson in a third-round match.
“It's related to the previous injury I sustained almost four weeks ago... in Delray Beach,” he told reporters.
"It's the same muscle in the hamstring, up high. It got progressively worse after my first round. It seemed like it was not possible for me to compete today without putting myself at significant risk."
Raonic said he would not return until he felt 100 percent fit again.
"That could be in two weeks; that could be a little bit longer."
(Reporting by Gene Cherry in Salvo, North Carolina; Editing by Clare Fallon)
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