Day's biggest issue was with his driver and no shot showed that more than his tee shot on 14 when he hooked it into the lake on his way to his 4th bogey off the day.
"It's just one of those weeks, and now I'm on to the next week, which is nice", he said.
Wise, seeking his first PGA win, fired a 68 to settle for a career-best second on 274 with Watney, who was chasing his sixth PGA title and first since 2012, closing with a 60-foot birdie putt to match him for the runner-up spot.
England's Paul Casey was the top European on seven under - good enough for a share of fifth alongside Americans Phil Mickelson and Peter Uihlein.
He won the Players back in 2016 and now has to be one of the favorites to win it again.
Day made birdie on 16 and then hit the flagstick on the par 3 17th green to give him another birdie.
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They got their legs under them in the second, scoring four of their own on route to seven total goals. Predators forward Nick Bonino told reporters there's no great secret to the club's road success .
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"What I did today was a bit out of the ballpark, in terms of off the tee", Day acknowledged after carding a two-under 69 to finish at 12 under. Aaron Wise made a remarkable up and down on 18 and Nick Watney drained a long putt to them both at 10-under par.
Woods has missed the tournament the previous two years but returns this time around, while Si Woo Kim heads to the event as defending champion after his history-making win in 2017.
"That is what I am most happy about", Day said.
Close-range gains at the seventh and eighth put the 30-year-old back on track and after another birdie on the 10th, Day overcame bogeys at the 13th and 14th.
It was a disappointing week for Tiger Woods, meanwhile, as he ended on two over after a birdie-less final round.
Woods challenges the tour's top talent again starting Thursday at The Players Championship, when he will be paired alongside fellow former Players champions and USA compatriots Phil Mickelson and Rickie Fowler.