Fleisher dominated the tour when he turned 50, winning seven times in 1999 and four more times in 2000.
He turned 63 last October and a win here would allow him to break the record of Mike Fetchick -- who won in 1985 on his 63rd birthday.
Fleisher, whose last victory came in 2004, shot a 6-under 65 at the TPC-Tampa Bay course, one shot better than Michael Allen and Chien Soon Lu.
Andy North, the winner of two U.S. Open titles among his three career victories on the regular tour, shot a 68 in a rare Champions Tour appearance.
Sandy Lyle, who shot 86-78 in his two rounds at the Masters last week, posted a 69 that left him tied for 13th.