Day hit a number of clutch shots in overtime, including the 113-yard wedge into the 18th green to set up a tieing birdie on the last hole played on Sunday before the playoff was suspended due to darkness.
World number 14 Day's USA title total, topped by his 2015 PGA Championship title, also includes the 2015 Torrey Pines crown, putting him alongside such two-time winners as Arnold Palmer and Tom Watson.
They each made birdie three times on the par-5 closing hole in the playoff.
American Ryan Palmer was also in the playoff after the trio finished at 10 under, but he was eliminated on the first playoff hole.
5- 18th hole: Day finds a fairway trap and Noren hits the green in two, applying the pressure. Wood finished tied for 23rd at three-under par.
"I wish I would have birdied in regulation, that would have taken care of business", Day said. Day made his birdie putt for the win.
"It has been a long time coming", said Day, who battled a back injury at the start of the week and missed the pre-tournament Pro-Am.
"I just got up and just kind of saw the yellow a bit and just hit it, and I'm like, I said "sit", but I didn't know where I was".
Yesterday, Day pulled his tee shot well right to begin the sixth playoff hole while Noren found the edge of the short rough left of the fairway. Noren, the 54-hole leader, shot a final-round 73, while Day shot 70.
"That double was very sour to me", said Noren, ranked 19th in the world. It's just margins, said Noren, a nine-time European Tour victor seeking his first United States triumph.
After losing his 47-week stranglehold on the world No.1 ranking to Dustin Johnson last February, Queensland native Day says his 11th PGA Tour victory marks the return of his world-beating 2015 form.
Woods said it was a mostly positive week, and it was hard to argue considering he was returning from his fourth back surgery.
But there won't be any spectators allowed at Torrey Pines today.
"To win would be very, very big for my confidence", he said. "I had my best mate on the bag and it was a nice way to go".