The three-time PGA Tour winner used the fortunate break to set the stage for a bogey free four-under-par 66 in delightful conditions at the TPC River Highlands in Cromwell.
He posted a 13-under 197 total, while Australian Aaron Baddeley notched a 65 to move into second place on 12-under.
It is anything but a two-man race, with Spaniard Sergio Garcia, South Korean K.J. Choi and Americans Scott Langley and Michael Putnam two shots behind in the PGA Tour event formerly known at the Greater Hartford Open.
Moore, 31, is a former U.S. Amateur champion who has compiled a solid professional career without quite living up to the expectations of greatness that some expected.
He said his round was an example of scoring well without being at the top of his game, and his eagle at the par-five sixth was clearly the highlight.
He blocked his drive to the right but his ball “chased down the cart path” and left him only 227 yards from the hole.
“It (the ball) was still sitting on the path but I had a reasonable opening, had to cut it a little bit, but decided to hit it off the path,” he told CBS television.
“I knocked it right up there with a hybrid to the front edge and was able to topple that one in (with a putt from 35 feet).
“I can’t say I hit it amazing today but sometimes you just get it around.”
Baddeley is another former young phenom who won the 1999 Australian Open as an amateur before successfully defending as a professional the following year.
He moved into the hunt for his fourth tour title, less than a year after being mired in such a slump that he barely kept his tour card.
World number eight Garcia made his move with four birdies in the final eight holes to card a 65.