Reigning Masters Tournament Champion Reed made four birdies in six holes on the back nine to sign for a 67 and set the target at 14 under, with Willett making three in a row from the 14th to join him with a 68 at the eighth Rolex Series event of the season.
England's Jordan Smith produced a big finish of his own to get to 13 under, one shot clear of countrymen Matt Wallace and Lee Westwood, and South African Dean Burmester.
In the battle to win the Race to Dubai, Francesco Molinari was on course to take the title, with closest rival Tommy Fleetwood eight shots off the lead and needing a win.
Reed is looking for his first victory since he donned the Green Jacket in April, while Willett's last win also came at Augusta National in 2016.
“I feel good,” said Reed. “I feel like the consistency of my game is where it needs to be. To have a chance to go out and finish the year off right and win a golf tournament, give myself a little early Christmas gift, a trophy, would be amazing.”
Wallace entered the day with a one-shot lead and when he holed a 15-footer on the first, got on the green at the par-five second in two and played a brilliant bunker shot on the third, he made a three-birdie start and led by three.
A double-bogey on the eighth stalled his progress, however, and the day developed into a battle between Reed and Willett in the later stages.
Reed sandwiched a bogey on the fourth with birdies on the two par fives on the front nine before a 15-footer on the 11th had him one off the lead.
A wonderful 25-foot left-to-righter on the 13th put the American in a six-way tie for the lead and an excellent chip on the next set up another birdie. A 15-footer on the 16th handed him a two-shot advantage but Willett soon set about reeling him in.
The 31 year old holed a six-footer on the fifth and made the most of the seventh but when he got in tree trouble off the tee at the 12th, he did not look likely to challenge.
The Englishman bounced back on the par-five 14th, however, before putting an approach to five feet on the next and holing a 20-foot left-to-righter on the 16th.
“There's a lot of golf left,” said Willett. “A lot can happen in 18 holes.
“I'm just happy with the golf game. The golf game is in good shape, the body is feeling good and it's been a long old year with all the stuff that's gone on. For this to be the last event I'm going to play in this year with a field this good is a real bonus.”
Smith joined the lead after birdies on the second and eighth on a front nine that saw him also birdie the seventh but bogey the sixth and ninth. He dropped a shot on the 13th but bounced back with two birdies before a lovely chip on the last set up a closing gain.
Wallace slipped back to level par on the day with a birdie on the 13th but he hit back on the next in a 71.
Full of confidence after last week's stunning victory at the Nedbank Golf Challenge, Westwood got off to a flier, with a long putt from off the green on the first and brilliant iron play on the second and third bringing three birdies. A 12-footer on the fifth handed him another gain and he sandwiched birdies on the 11th and 14th with a tee-shot to tap-in range at the par-three 13th.
Burmester only played his way into the field last week but finished fourth here last season and carded six birdies and two bogeys on Saturday in a 68.
Spaniard Adrian Otaegui was a picture of consistency until recording a closing bogey in a 71 to sit at 11 under alongside England's Tom Lewis, who carded a 67.
Shubhankar Sharma tightened his grip on the Sir Henry Cotton Rookie of the Year Award with a 66 that left him in a heavyweight group alongside reigning champion Jon Rahm and Major winners Sergio Garcia and Henrik Stenson at ten under.