Day, a semifinalist last year, led from the start in a 3-and-2 victory over Rickie Fowler.
Dubuisson became the fourth player to reach the championship match on his debut in the 15 years after this World Golf Championship began in 1999. He had to take down Ernie Els in the most compelling match of the morning on Dove Mountain.
Els, trying to reach the final for the first time, went 3 up through four holes and was on the verge of stretching his lead until the 23-year-old Frenchman halved the hole with a tough par putt at No. 7. Dubuisson won four of the next five holes to take the lead, only for the 44-year-old Els to battle back.
Els made a 20-foot birdie putt on the 16th to square the match, and they headed to the 18th hole. Dubuisson hit to the back fringe, while Els came up short with a 6-iron into the breeze and found a bunker. He blasted out to just outside 12 feet, and narrowly missed the par putt to extend the match.
Dubuisson said he didn't sleep well Saturday night and didn't feel well when he arrived at the golf course, perhaps because "I realized I was in the semifinal of the World Golf Championship against Ernie Els."
"I'm a big fan of Ernie, so I have always been watching him winning majors," he said. "I knew I had to play my best golf. It's what I did."
Dubuisson is the first player since Geoff Ogilvy in 2006 to reach the final match in his first time playing this event. Ogilvy went on to win the title.
It was a big blow to Els, who badly pulled an 8-iron far left of the flag on the 17th, losing a chance to put pressure on Dubuisson, and then came up short on the 18th.
"It's tough to take," said the four-time major champion.
Day won the opening hole with a birdie and never looked back, though Fowler didn't give in.
Day was 3 up through 11 holes when he missed a 6-foot par putt on the 12th and Fowler made birdie on the 13th to cut the deficit to one hole. The turning point came at the 15th, when Fowler missed far enough left with his drive that he had no shot at getting close. He hit a flop shot strong that went over the green, hit another strong pitch and missed the par putt.
Fowler had a chance to go 1 down on the 16th with a tee shot into 6 feet. But he missed the birdie putt, and then missed the 4-footer coming back for par to end the match.
"The start of the season, that's all I'm trying to do is win," said Day, with only one PGA Tour victory in his career. "I felt like I had a really good chance at maybe having a shot at winning this week and I'm definitely in the final now and I'm really looking for to it."