Poston drove into the water that lines the right side of the par-4 18th at Keene Trace and made a bogey on the final extra hole. Power hit the fairway, played his second to 12 feet and two-putted for the victory.
Power birdied the par-3 16th and the 18th in regulation for a 5-under 67, with the 34-year-old Irishman posting at 21-under 267 while Poston was squandering the lead behind him.
Poston had a double bogey on the par-5 15th after driving an inch out of bounds to the left, then followed with a three-putt bogey on the par-3 16th. He parred the final two holes for 70.
On the first extra hole, Power holed an 18-foot birdie chip from the collar of the 18th green and Poston matched him with a 10-foot putt. They matched pars on the next four holes, on No. 18 again, then twice on the par-3 17th, and again on 18.
Because the tournament was played opposite the British Open, Power did not earn a spot in the Masters with the victory.
The 28-year-old Poston missed a chance for his second PGA Tour title. He won the 2019 Wyndham Championship in his home state of North Carolina.
James Hahn followed a career-best 70 with a 70 to tie for fifth at 19 under with Patrick Rodgers (67), Henrik Norlander (67), Ryan Armour (68), Mito Pereira (67) and Luke List (71). Hahn bogeyed the final two holes.