Last year's runner-up and fourth seed Norwegian Casper Ruud advanced to the next round by thumping Swedish qualifier Elias Ymer 6-4 6-3 6-2
Darkness halted their duel after five extra holes Sunday at Torrey Pines South Course after each finished 72 holes on 10-under par 278.
It was Day's 11th US PGA victory and his first since the 2016 Players Championship.
"It has been a long time coming," Day said. "It's special because I worked very hard in the off-season to get back in this position."
The triumph came after Day withdrew from a Wednesday Pro-Am with back issues that had him wondering if he could even compete after an MRI on his back 10 days earlier.
"I was in Palm Springs and I threw it out," Day said. "I'm always going to try to maintain and be on top of it."
He found bulging discs that can hit nerves under the stress of shotmaking. "When they get bigger they get closer to the nerve and I get shooting pains down my legs," Day said. "I just have to keep my core strong and hopefully I'm out here battling when I'm 40 or 45."
The playoff continued at the par-5 18th hole, which both players birdied three times earlier in the playoff. The also parred 16 and 17 once in Sunday's late-day drama.
On Monday, 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 blasted his second shot onto the raised green but the ball rolled back into a water hazard, prompting Day to leave his second shot short of the water.
"I'm not regretting my decision. It's just margins," said Noren, a nine-time European Tour winner seeking his first US triumph.
"I had the perfect yardage to the pin with the 3-wood, 230 metres. I had the advantage I thought. If I hit a good one it would hit the back of the green. If I hit it short it would be perfect."
Day rolled his approach inside of two feet from the cup, forcing Noren to try and hole his 40-yard pitch and run shot for birdie. He ran the ball well past, missed a long par putt and took the bogey before Day's victory tap-in.
"We just had to stay patient," Day said. "My goal is to get to number one and this is a start in the right direction.
"I've just got to take it in right now. I was up all night thinking about trying to get that 11th win."
World number 14 Day's US 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.
Last year's runner-up and fourth seed Norwegian Casper Ruud advanced to the next round by thumping Swedish qualifier Elias Ymer 6-4 6-3 6-2
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