Fleisher boasts a remarkable record at this event, having won here in 2000 and finishing second in his two other appearances.
'I'm in position but there's a lot of guys within about four shots,' said Fleisher. 'This is a golf course where if you feel comfortable you can shoot a low number.'
The 2001 U.S. Senior Open winner began the day two strokes behind overnight leaders Dana Quigley and 63-year-old Mike Hill and made his move on the front. He picked up ground with a birdie at the fourth and added two more from the sixth to make the turn at minus 8.
Fleisher remained in a comfort zone on the back nine rolling in three straight birdies from the 12th, including an eight-foot putt on 14 that gave him the outright lead at 11-under.
He ran into trouble with a bogey on the following hole to fall back into a tie for first. At the next, Fleisher hit his approach to within 10 feet of the hole to regain the lead.
'I'll try to shoot the lowest I can,' said Fleisher of his chances Sunday. 'I hope the golf gods are with me.'
The top spot on the leaderboard was clogged with several players at a time, including Kite. The 52-year-old played alongside Fleisher and had some early success with two birdies before running into trouble with a bogey on the fifth.
Kite birdied the seventh and made a putt from outside 40 feet for the first of back-to-back birdies from the 11th. He added another birdie on the 14th to briefly grab a share of the lead at minus 10.
The four-time Senior Tour winner then had a chance to tie Fleisher at 11-under but failed to convert on an 18-footer for birdie on the 16th.
'I'm playing pretty good golf but I can't seem to catch the leader,' said Kite.
Bruce Summerhays started the day one shot behind the overnight leaders and grabbed a share of the lead at 10-under with a birdie at the 12th. However, the 58-year-old dropped a shot at 15 to fall two off the lead.
Doug Tewell had five birdies and one bogey for 67 and moved to 8-under 134, one shot clear of the first-round leaders.
Quigley hit his approach to within five feet for birdie on the par-5 14th to move into a share of the lead at 10-under before running into trouble on the following hole. A bogey on 15 dropped him to 9-under and a double bogey two holes later gave him a round of even-par 71 and a two-day total of 7-under 135 along with Hill (71).
Full-field scores from the Verizon Classic