The 21-year-old former NCAA champion Wise shot a closing 68, while Watney holed a monster birdie putt on the last for a 69 to join him on 10 under, with Bryson DeChambeau a shot further back in fourth.
The Australian shot a four under 67 on the third day at Quail Hollow after recovering from a poor start to move to 10 under overall.
If you haven't noticed by now, Jason Day tends to play his best golf on some of the toughest venues on tour, having earned hard-fought victories at courses like Torrey Pines and TPC Sawgrass.
In his mind, the pace of the greens is faster than they really are. "I'm hitting the ball well enough to contend, to win this golf tournament, but I just haven't made putts". I've had ample time to make the adjustment, and I just haven't. I'm still hitting it high where I can stop it and there's six less spin. Day finished No. 1 in strokes gained around the green and No. 2 in strokes gained putting on the week. He was tied for 24th at the Farmers Insurance Open, missed the cut at the Genesis, finished 12th at the Honda Classic, tied for second at the Valspar Championship and tied for fifth at the Arnold Palmer Invitational. He made the putt to take a two-shot lead, becoming the only player to birdie the hole in the final round.
Tiger Woods opined on what it's like to be at the top and figure out what's next. His chip checked up about 8 feet short of the cup and he missed that. A birdie at the 10th got him to 12 under, but things almost turned disastrous a few holes later, when Day bogeyed the 13th and then badly hooked his drive into the water at the 14th.
"I'd like to be able to hit it a little bit straighter ... I got shut out".
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At least he has the weekend. He birdied 16 by sinking a 10-footer and survived a scare at the 230-yard par-3 17. He responded on the final three holes at Quail Hollow, the "Green Mile", playing them in 2-under. Watney, a five-time victor on tour, is finally fully healthy and looking to get back to his winning ways, with his last victory coming at the 2012 Barclays at Bethpage Black.
The four-time major victor tumbled down the leaderboard on Friday after shooting a disappointing 76 to move over par, however, the County Down golfer has fought back to three under par and sits in a tie for 16th place, seven shots off leader Jason Day.
Woods said he remembers the speed of the bent grass greens in 2012.
He can, however, use Saturday's effort as a springboard to enter the week of the Players Championship in a confident frame of mind.
This is a new course to him.
He hit the next one across the green to 40 feet, and knocked that in for bogey. "I'm super, super excited", Watney said. "I missed so many putts".
"One of the best wins I have ever had", said Day, who never felt on top of his game Sunday.