On a crisp and clear morning in Arizona's high desert, Day sealed the win when fellow 25-year-old Fowler surprisingly three-putted from just five feet at the par-three 16th.
Day, who recorded six birdies in 16 holes to reach the final for the first time, will face Frenchman Victor Dubuisson in the title match later on Sunday at Dove Mountain's Ritz-Carlton Golf Club.
Dubuisson, who had never previously played matchplay golf until his debut this week in a World Golf Championships (WGC) event, came from three down after seven holes to beat veteran South African Ernie Els one up.
"It was a tough day," Day, who was beaten by eventual champion Matt Kuchar of the United States in last year's semi-finals, told Golf Channel.
"Rickie is playing great golf right now and I just thought if I gave that little bit of an inch for him to move in, he was going to knock the door down.
"So I was just trying to hang tough and my game was solid today. Hopefully I can take it into the final."
Day birdied four of the first eight holes to go three up before Fowler twice trimmed the lead to two, first with a concession at the ninth and again at the short 12th, where Day missed a seven-foot par putt.
The Australian also bogeyed the 13th for his advantage to be cut to one before getting back to two-up with a birdie at the driveable par-four 15th, where he chipped to three feet.
Fowler responded with a brilliant tee shot to five feet at the 16th but squandered the chance to level when he pushed his birdie attempt to the right of the cup, then missed the par putt coming back to lose the match.
In the second semi-final, four-times major winner Els raced into a three-up lead after just four holes against a slow-starting Dubuisson before the Frenchman got into his stride with birdies at the eighth and ninth to trail by one.
Dubuisson levelled the match with another birdie at the par-five 11th, where he chipped to within three feet, and went one ahead when his 44-year-old opponent bogeyed the 12th.
It looked likely that Els would get back to all square after he hit a stunning approach to a foot for a conceded birdie at the par-five 13th, but Dubuisson coolly matched him by sinking a clutch putt there from 18 feet.
However, the Frenchman stumbled at the par-four 14th where he failed to reach the green in two, executed a poor chip and ran his par putt well past the cup before conceding the hole.
Dubuisson got back to one up with a birdie at the 15th where his tee shot ended up just short of the green but Els immediately levelled when he stunningly drained a curling downhill birdie putt from 32 feet at the 16th.
Both players parred the 17th but the South African lost the match on the 18th green when he missed his par putt from 13 feet after the Frenchman had lagged his birdie putt to within two feet of the cup.
Dubuisson, who burst into the limelight by winning his maiden European Tour title at the Turkish Airlines Open in November, admitted he had been very nervous competing against one of his golfing idols.
"I didn't sleep very well last night, I slept like one hour, and this morning I woke up and I realised that I was playing against Ernie Els, one of my favourite players," the 23-year-old said.
"On the first tee. I shake the hand of Ernie and I wasn't feeling comfortable. I was watching him and I was very impressed to be next to him. I was thinking of all the matches he won and the (two British) Opens."
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- Ernie Els
- Victor Dubuisson