Doug Tewell shot a 5-under 66 to finish four shots off the lead at 7-under par.
'No question this would be a neat win,' said Doyle, who set a new 18-hole tournament scoring record.
Doyle was four shots behind overnight leader Fleisher to start the second round at Nashawtuc Country Club and, after weather delayed play early on for the second day in a row, he began his surge with three consecutive birdies starting at the par-4 first.
He ran home a 10-foot putt from off the green for a birdie at the par-5 fifth and drained a 12-footer from the fringe for a birdie at the par-3 eighth. Doyle then dropped his approach inside seven feet at the ninth for another birdie to go out in 29.
Doyle found trouble with a bogey at the par-4 12th but picked up back-to-back birdies from the par-4 14th to reach 10-under.
At the par-3 17th, Doyle dropped his tee shot inside 12 feet for a birdie to secure the 36-hole lead.
'Just seems like when I need something to go right it didn't this year,' said Doyle, who is seeking his first Champions Tour victory since 2001. 'You get into ruts like that. I'm doing things well and just not winning.'
Gilder was neck and neck with Doyle throughout the round and had a hot start of his own. He picked up a birdie at the second and followed that up with a birdie at the fourth.
At the par-5 fifth, Gilder reached the green in two and rolled in an 18-foot putt for an eagle. He hit his second to three feet for a birdie at the sixth to move to minus-8 and continued his fine play on the back side with a birdie at the 10th.
Gilder stumbled with a bogey at the 11th but countered with a birdie at the very next hole. He collected another birdie at the 17th but dropped a shot at the last to finish two strokes behind Doyle.
'Still upset about the bogey at 18. I hit the wrong club,' said Gilder. 'Should have hit one more club. All in all a good day.'
Bob Eastwood, Mike McCullough, Dick Mast, Dave Stockton and David Eger finished tied at 6-under-par 136.