Garcia's surprising concession on the seventh at Dove Mountain was the story of the day in Arizona, as the Spaniard gave Fowler a share of the hole, only to end up losing to the 25-year-old American on the 18th.
Fowler was two down at the seventh and faced a 17-foot par putt when Garcia, who stood over a four-foot attempt for par, offered to split the hole.
The 34-year-old Spaniard said he felt guilty about how long it had taken for him to take a drop on the previous hole and explained to Fowler that he wanted to halve the seventh to clear his conscience.
Garcia requested a free drop on the sixth hole, as his initial lie was very close to a bee hive on the edge of the green.
An astounded Fowler accepted the offer on the seventh hole and while Garcia won the eighth to go three up, the American responded on the next two holes, before winning the 16th and 18th to advance to the final eight.
Afterwards, Garcia - who had a public feud about sportsmanship with Tiger Woods last year after the Players Championship - claimed he did not regret his decision and could not help having a dig at the world number one.
"I don't regret it at all, he (Fowler) played much better than me on the last 10 holes and he deserves the win," Garcia said.
"This is a gentleman's game and lately it hasn't felt like it's been like that. This is the way I was brought up by my dad; I felt like my drop on six took too much time.
"If I had been in his position I would not have enjoyed waiting so long to hit my birdie putt after the great shot he hit.
"I thought it was the only thing I could do on seven to make myself feel better and not feel guilty about anything.
"I was playing as hard as I could and got three up but he started making birdies and I wasn't able to keep up."
Fowler's win will see him take on Jim Furyk in the final of the Ben Hogan bracket after the latter defeated Harris English one up.
In the Bobby Jones bracket, Oosthuizen eased into the final with a 5-and-4 win over Simpson.
Oosthuizen recovered from being one down after five holes to win six of the next nine and triumph on the 14th.
The 31-year-old South African will face Australia's Jason Day on Saturday, after the world number 11 defeated George Coetzee 3 and 1.
Graeme McDowell of Northern Ireland stayed alive on Friday, overcoming 2012 champion Hunter Mahan over 21 holes.
Astonishingly, McDowell has yet to lead heading to a hole at Dove Mountain this week but prevailed against Mahan despite trailing by two with two holes to play.
France's Victor Dubuisson will be McDowell's next opponent in the Sam Snead bracket after the Frenchman overcame Bubba Watson 1 up.
In the Gary Player bracket, Jordan Spieth will play Ernie Els on Saturday.
Spieth defeated reigning champion Matt Kuchar 2 and 1, while Els beat Jason Dufner 1 up.