The American youngster was tipped by Coley at 80/1 each-way in his pre-tournament preview but he's now just 6/1 after a third-round 66 ensured he would enter the final round in a three-way tie for second along with Webb Simpson (7/2) and Kevin Na (6/1).
The stoic Swede birdied eight holes in Round 3 to offset two bogeys and a double-bogey.
"Keep making birdies, stay aggressive and know that there's plenty of good golfers behind me", Simpson said. "The putting has been solid".
"I wasn't swinging my drivers as well as I did yesterday, and that made it hard to adjust the distance of my iron shots". There were a couple of swings here and there that were not to satisfaction. It's nice to feel it, whatever it is.
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Simpson, the 2011 champion, led late in the round until a bogey at the 17th.
But the day belonged to Armour, who recorded nine birdies - including four in a row from the fifth to the eigth - on his blemish-free scorecard. "I had some goals at the beginning of the week".
Languishing in 199th position, Harrington needs to either win the tournament or finish second to retain his PGA Tour card for 2018, though he does have a medical exemption following back surgery in March which will entitle him to play in nine tournaments next year should he miss out this weekend. "That's all I can do".
Henrik Stenson was a stroke behind them after a 66. He added six more on the round, including four on his first six holes of the home nine.
Davis Love III, who has won in Greensboro three times, and Gastonia's Harold Varner are at 13 under with Richy Werenski. He could have ended his round with another one, but pulled his 15-foot birdie putt wide right and settled for par.
"I hit a lot of good shots out there", Stenson told Sky Sports.
Irish pair Shane Lowry and Seamus Power both carded three-under 67s as Graeme McDowell, needing a strong week to have any chance of reaching the FedExCup play-offs, struggled to a one-over 71.