Five extra holes were needed at Dove Mountain as Day claimed a win in the final over Dubuisson, who twice saved the match from seemingly impossible positions on Sunday night.
"Vic, man, he has a lot of guts," Day told journalists. "He has a great short game - straight out of the cactus twice. For a 23-year-old kid, he's got a lot of game.
"We're going to see a lot of him for years to come."
Day moves up to fourth in the world rankings thanks to the win in Arizona.