Hale Irwin, who was also through 15 holes when play was called, was one behind Fleisher at minus-5. First-round leader Mike McCullough, who was playing alongside Irwin, is at 2-under par.
The tee times were pushed up on Saturday at the TPC of Tampa Bay in anticipation of inclement weather. When storms rolled into the area in the afternoon, the round was called with 16 players left on the course. They will return to complete the second round Sunday at 8:00 A.M. ET.
Fleisher was one shot behind McCullough to start the day and picked up two birdies and one bogey on the front side to make the turn at minus-4. He bogeyed the 10th but responded with a long birdie at the 11th.
The 54-year-old got up and down for birdie at the 12th and hit a wedge to four feet at the 13th to make it three in a row.
'I really played well,' said Fleisher, who won this event in 2000. 'I would have liked to have finished.'
Irwin had a birdie and a bogey on the front side and got a boost with an eagle at the par-5 12th. He followed that with a birdie at the 13th but dropped a shot at the 14th.
'If I can hit the ball tomorrow like I did today, I'll be happy,' said Irwin. 'I wasn't that aggressive today. You've got to have a lot of patience today. Lots of challenging predicaments that we all get ourselves into. I hated to hear the siren.'
Wayne Levi, who turned 51 today, is the leader in the clubhouse at even-par 142. Tom Kite is at even-par through 15 holes. Only five players were at par or better when the second round was halted.
Des Smyth carded an even-par 71 to finish in a group at 1-over-par 143 along with Jim Thorpe, Dana Quigley and Allen Doyle. Mike Hill is 1-over through 16 holes while Mark McCumber is also plus-1 through 15.