Bradley held a four-shot lead after rounds of 65 and 66 but stumbled home in 41 with a double bogey and three bogeys on the back nine to finish nine under par.
That left the former US PGA champion three shots behind Moore and Stroud, who carded rounds of 69 and 68 respectively to lead by one shot from fellow American Gary Woodland (67) and Thailand's Kiradech Aphibarnrat (69).
Moore was six under for his first 10 holes before also struggling on the back nine, dropping shots at the 12th, 13th, 15th and 16th - twice finding greenside water hazards - although he did birdie the 14th.
"It was almost two different days out there," Moore said. "I'm rolling it well and if I'm putting well I'm going to have opportunities. I know I'm going to make some birdies."
Stroud, who lost in a play-off to Ken Duke in the Travelers Championship earlier this year, will be looking for his first victory on the PGA Tour on Sunday.
"I'm pulling from all that experience and what I learned under the gun (at Travelers) was I don't need to try to do anything fancy," Stroud said.
"I just need to stick to my game plan, keep hitting shots, keep hitting good quality shots, keep putting myself in the right positions, keep hitting good putts, and stick to my strengths, which are chipping, putting and wedges, and get myself in the fairway."
Woodland's 67 was the joint second lowest round of the day and came courtesy of a putting lesson from Open champion Phil Mickelson, who is five off the lead after a 68.
"I've been playing good for a long time, I just haven't been putting it great and got a little putting tip from Phil actually this week, and it's been working pretty well," Woodland said. "I'm excited about that."