The pair played five extra holes before agreeing it was too dark to continue on Sunday. American Ryan Palmer was eliminated from the playoff at the first extra hole after failing to match the birdies carded by the other two.
Australian Day shot a closing 70, Noren of Sweden a 73, and Palmer carded a 72 as the trio finished at 10-under 278.
Only five extra holes were possible due to a slow final round, with the final threesome taking five hours and 55 minutes as whipping winds prompted plenty of indecision.
J.B. Holmes, who finished a stroke outside the playoff, took more than four minutes to play his second at the par-five 18th.
Day said he was ready to go the distance on Monday in order to get his first win since the 2016 Players Championship.
"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," he said.
"This is something new for me to be able to go through a playoff and come back the next day.
"Man, this is stretching out a little longer than I wanted but I just want to get that 'W' real bad."
Noren had one hand on the trophy when he wedged his third shot to tap-in distance at the first extra hole, the 18th, but Day matched the birdie by pouring in an eight-footer.
An hour later they remained deadlocked after both players sank five-footers in the semi-darkness on the fifth extra hole.
"I could barely see the last putt but this is what I play for, so I'm excited," Noren said.
"It's better this way (returning on Monday) than maybe missing a short one when you can't see."
The playoff will resume at 8 a.m. local time (1600 GMT).
Tiger Woods, meanwhile, continued his promising comeback, finishing only seven strokes off the pace in a tie for 23rd.
Woods, 42, underwent a spinal fusion last April and made his comeback at the unofficial Hero World Challenge in the Bahamas in December, tying for ninth of 18 players.
(Reporting by Andrew Both; Editing by Clare Fallon/Peter Rutherford)
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