Day, who will become world number one in the new rankings after his strong showing this week and victory at the Arnold Palmer Invitational last week, will face South Africa's Louis Oosthuizen in the final later today.
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Former Open champion Oosthuizen booked his place in the final with a 4&3 success over Spain's Rafael Cabrera-Bello at Austin Country Club.
The other semi between two of the world's top three players was much closer. McIlroy led by one at the turn, but Day then won three of the next four holes to go 2 Up with five to play.
McIlroy got one back straight away, but the last four holes were all halved as Day sealed victory with a 12-footer on 18 after McIlroy failed to find the green with his approach from a fairway bunker.
McIlroy, who won the tournament last year, misses out on equalling the longest unbeaten run in the tournament held by Tiger Woods. He and Cabrera-Bello will play again for third place.