|McIlroy shares a laugh with Woods during their match Thursday. (Getty Images)|
The two Englishmen, who played on the victorious European Ryder Cup team, will meet Saturday, with the winner getting $1.5 million and the runner-up $1 million in the eight-player exhibition.
Rose, who holed a sand wedge shot for an eagle at the 14th, finished with a 2-under 69 while Woods was at 70.
Westwood shot a course-record 61 in the semifinals to beat 2011 Masters champion
"It was just one of those days I was on a roll. I am just pleased to be swinging the ball well because I've got no hangover from the Ryder Cup, and that's nice," Westwood said. "It seemed the hole just got bigger and bigger with each hole I played, and that hasn't happened for a while.
"It's also a very satisfying feeling to be playing in a tournament like this, and if Justin had not beaten Webb Simpson earlier today I would not have had the opportunity to go out and shoot 61. So a lot of things have to go your way and I have capitalized on a bit of fortune."
Rose tried to pull his cap over his face when his wedge shot at No. 14 took a couple of bounces and disappeared into the hole. Woods also broke out in a smile.
"I was really struggling early on today and to can that shot at 14 was easily the turning point," Rose said. "In proper match play you would only win the hole, but in this format I've picked up two shots on Tiger and it's help me win the match."
Rose then birdied No. 13, and after his eagle a hole later both birdied No. 16 before ending with two pars apiece.
"When Justin birdied 13 and holed out at 14, it was the turning point in the match," Woods said. "I was 2 up at the time and all of a sudden 1 down with four holes to play.
"But I haven't played this format since the Dunhill Cup in '98, so it's been awhile, and it's a neat format as it's never over until it's done. There can be some big-time swings out there, as we saw with Justin at 14. But then it was a long day and it's certainly frustrating when I've lost two matches by a shot, but that's the way it goes."
Rose is now ready for an all-English showdown with Westwood.
"I would dearly love to win this as I want to stay fresh and I want to stay hungry for the rest of the season," Rose said. "There is very little history of Westwood and myself playing against each other, but being the world No. 5 at the moment it would be great to get one over the world No. 4."
The final is Saturday morning, with Woods and the other players competing in an afternoon pro-am. Woods has hinted he will consider a return to Turkey next year for the inaugural $7 million Turkish Open that was announced this week.
Woods also backed Darren Clarke to become captain of the European team for the 2014 Ryder Cup in Gleneagles. Woods helped Clarke when the Northern Irishman's first wife, Heather, died weeks before the 2006 Ryder Cup in Ireland.
"I'm not sure what the process is, but if Darren is selected he would make a great captain," Woods said. "He's one of my best friends out here and he's a great guy. He'd make a great leader."