Fisher won 1-up after Cabrera needed five shots to reach the green on the final hole. Fisher had sent his second shot from 244 yards within 5 feet of the pin in fading light at the Finca Cortesin golf course.
Kim advanced by beating Robert Allenby 5 and 4. Kim, who beat the Australian 5 and 3 at the Presidents Cup, rallied from an early two-hole deficit, pulling away at the 27th hole when he holed an approach from 101 yards.
The American first overcame an errant tee shot on the 26th to save par and halve before holing out from 101 yards for an eagle at 27. He sank a birdie putt on the 28th for a four-hole advantage.
Kim cited his par save at the 26th was the key.
"That was the hole that really sealed it for me," he said.
Fisher sank birdie putts at the 32nd and 33rd holes to get ahead before Cabrera forced the playoff by sending his second shot from the thick grass at the last hole within 5 feet of the pin. Fisher missed his birdie attempt from off the green to set up sudden death.
"I figured he was going to go for it, but it was a high-risk shot and the odds of him pulling it off were slim," Fisher said. "I saw him hit it and then I heard the cheers and I thought 'Oh my dear.'"
Both players missed winning putts on the first playoff hole.
Sunday's 36-hole final will be both player's first in their debut appearance in the event, with a $1.1 million prize on the line.
Kim barely held on to his driver at the 26th as his ball sailed left into the bushes.
After taking relief, he pitched to 2 feet for his par, while Allenby missed a chance to trim the deficit to one hole by flubbing a chip and then pushing his birdie putt wide.
"What happened was pretty crucial because he gave me a gift," Kim said. "He just miss-hit his chip a little and made par."
Kim was elated at the 27th - a short par 4 - after his sand wedge landed a few feet long before back-spinning into the hole. He then sank his birdie putt on the 28th for a four-hole advantage over Allenby, who missed from 4 feet.
Allenby missed several opportunities to get within one before Kim boosted his lead.
"The putter was pretty cold this afternoon," Allenby said. "I just didn't quite play good enough this afternoon and, you know, he hit a lot of great shots and made a lot of good putts."
Kim cruised from the 30th after taking a 5-up advantage.
"This is a very big tournament for me because it's been a very tough year," said Kim, who a day earlier won his last hole to ensure his place in the last four. "It's very rewarding to come out here ... and put on a good show."
Fisher, who finished fourth at the Accenture Match Play Championship earlier this year, finally got ahead on the 25th hole and was 2-up after 27.
Cabrera battled back to even it on the 30th and was 1-up after Fisher bounced his drive off a cart path and into the trees on his way to a bogey on the 31st. But the Englishman soon took over.
"I fought back really well in the morning to give myself a great chance in the afternoon," Fisher said.
The last American to win the event was Corey Pavin in 1993. Shaun Micheel reached the final in 2006.
Copyright 2009 The Associated Press.