McIlroy, the second-ranked player in the world, defeated world No. 3 Lee Westwood, 3 & 1, in their highly-anticipated match.
Now, if McIlroy can beat Mahan Sunday afternoon, McIlroy, the reigning U.S. Open champion, will become the No. 1 player in the world rankings Monday morning.
Mahan knocked off Mark Wilson, 2 & 1, in the less-vaunted other semifinal.
McIlroy was 3-down after four holes Sunday, but he won four of the next five to take an improbable 1-up lead. He appeared to be in trouble at the par-five 11th, but his ball hit a cart path and landed safely. He and Westwood halved the hole, which had to feel like a win for McIlroy.
"That was very big, it was very fortunate," admitted McIlroy. "That ball could have ended up anywhere."
McIlroy rolled in a 23-foot birdie putt to win 12, then benefited from an errant tee shot from Westwood at 13. Westwood's ball came to rest in a woman's sweater and all he could do was make par. McIlroy posted a birdie and moved 3- up.
Westwood rebounded a bit with a spectacular 20-foot eagle at the par-four 15th, but made a mess of 17. His approach came up short and when his eight- footer for par stayed above ground, he conceded the great comeback win to McIlroy.
"I was trying to stay patient," McIlroy said on TV. "I knew if I could just keep chipping away, I was thinking if I could get him square going into 14, 15 around there, it would be great.
"To go into those holes 3-up was a huge bonus."
Mahan won the first two holes of the semifinal, but Wilson won two of the next three. Mahan captured the other hole in that stretch to stay 1-up, but when Mahan won eight, he was 2-up.
Mahan was in close at 10 and Wilson missed the green. He chipped in and Mahan made his short putt to stay 2-up. Wilson won the 12th with a par to cut the deficit in half, but Mahan took the 15th to return to his 2-up advantage.
After the 16th was halved with pars, the two once again made matching pars at 17, giving Mahan his first appearance in the final.
"This morning was cold, it was tough," Mahan said in a televised interview. "I'm not going to change anything, try and hit fairways and greens."
Westwood will face Wilson in the third-place match Sunday afternoon.