Rory McIlroy won the first sudden-death hole on the resumption of his World Match Play tie against Paul Casey to set up a semi-final with Jim Furyk.
Casey said he felt ill overnight after their match was halted on Saturday after 21 holes because of poor light.
Both players reached the par-five first in two shots but while McIlroy judged the pace of his long putt beautifully, Casey duffed his chip from the fringe.
Northern Ireland's McIlroy holed a short birdie putt to progress.
"I feel very weak," said Casey, who had a two-shot lead after nine holes on Saturday. "It's unfortunate but in seasons as long as ours there are moments when you get sick.
"My expectations were low but it didn't stop me trying. I actually hit two great shots, there."
McIlroy said: "I didn't know Paul was unwell. But I've dug out another win, so it's made the early start worth it."
Of semi-final opponent Furyk, McIlroy added: "He can be a frustrating opponent. I hit the ball quite a bit longer than Jim, but he doesn't make many mistakes and I'll have to play well."
In Sunday's other semi-final, England's Danny Willett takes on American Gary Woodland.