After round four, Ryan Palmer joined the Australian and Swede on the extra holes after they all completed regulation play at 10-under 278 at Torrey Pines.
Palmer was knocked out on the first par-five play-off hole after both Day and Noren were one shot ahead of their rival with a pair of birdies.
After that it was impossible to determine a winner after both players matched each other shot for shot for a total of five holes.
Day came within inches of lifting the trophy with a birdie attempt on the par-four fourth hole of sudden death, but eventually time was called as Day made a 6ft birdie putt on the fifth, matched by a 5ft birdie from Noren on the par-five 18th in the fading light.
Speaking as dusk fell, Day told the PGA Tour website: “Alex is playing some tremendous golf. To be able to go shot for shot there was pretty special, so I’m just going to try to get some rest tonight and I’ll play all day tomorrow if I need to get the win.”
Earlier in the day, Tiger Woods recorded his best finish in a full-field PGA Tour event since August 2015, carding four birdies and four bogeys in a closing 72 for a three under par total.
That left him inside the top 30 – his best finish since tying for 10th at the Wyndham Championship three years ago.
Defending champion Jon Rahm had work to do after slipping to 12th place at the start of day four, but a run of four bogeys on the front nine left him on five-over 77 and further down the leaderboard tied for 29th by the end of regulation play – and ending his chance to become world number one.
Noren has won nine times on the European Tour – six in the last three seasons – and will continue to chase his first PGA Tour title when play resumes on Monday.
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