Day birdied the par-5 18th, the sixth playoff hole, for his first PGA Tour victory since the 2016 Players Championship and his second at the Farmers.
"It's been a long time (without winning) so happy to start off the year great", said Day, who also triumphed here three years ago.
Most of Day's equipment setup remained the same from the end of past year, with the exception of the driver.
"It's special because I worked very hard in the off-season to try and get back in to this position and I didn't realise I had a chance this week".
Day is the former world No. 1 who had fallen to No. 14 in the rankings. He's a nine-time victor on the Euro Tour in 246 career events, most recently the 2017 BMW PGA.
Five sudden-death holes couldn't separate the players before darkness saw play suspended late on Sunday, leaving the duo returning to play a fifth day at Torrey Pines.
He picked up where he left off on Monday, knocking another wedge to a couple of feet after Noren had splashed his second shot in the water.
Despite his success on the European Tour, Noren is little known in the United States - and he's happy to fly under the radar.
However, with light fading, the four-hole playoff has pushed play into an extra day and will resume on Tuesday morning (AEDT).
He was disappointed to give two shots back with a double-bogey at the 12th, where he needed four shots to reach the green.
"I thought if I hit a good one it would be back of the green", he said. I'm very thankful for my whole team.
Day joked that they could have continued to play, that all that was needed was some auto headlights along the fairway.