Three players held the previous record of 193, last matched by Gibby Gilbert in 1992. Fleisher fell short of the all-time Senior Tour record in relation to par, which is 22-under, last accomplished in 2001 by Tom Kite and Ed Dougherty.
Hale Irwin finished second at 14-under-par 196 followed by 2002 U.S. Senior Open winner Don Pooley, who posted a final-round 68 to come in at 12-under-par 198.
Fleisher opened with a birdie at the third, but ran into trouble with a three-putt bogey at the very next hole. He recovered with a birdie at the fifth, but faltered again with the putter at the ninth, needing three putts for bogey to make the turn at 16-under.
The 53-year-old almost found trouble again at the par-4 12th but sank a key putt to save par.
'The key to me was making the par-saving six-footer at No. 12,' said Fleisher.
After the save, Fleisher he hit a 5-iron to 12 feet for birdie at the 13th and stuck a 6-iron within five feet at the 14th to make it two in a row.
He closed out his round by sinking a two-foot putt on the final hole. With the birdie at the 18th, Fleisher tied the largest margin of victory at the RJR Championship. Lee Trevino won the 1993 tourney by five strokes.
'I can smile now, but do you ever get comfortable out there?' said Fleisher, who won for the 15th time on the Senior Tour. 'Maybe with a five-shot lead on the last hole. That's the only time.'
Fleisher opened the week with a 10-under 60 on Friday to match the Senior Tour's all-time 18-hole scoring record and followed with a 64 on Saturday to distance himself from the field. At one point Sunday, Irwin got within three strokes of Fleisher, but Fleisher was too much to overcome.
Irwin struggled early with two bogeys over his first four holes but recovered with a stretch of three consecutive birdies from the fifth to make the turn at 13-under.
'I thought that his 60 could win the tournament if he played respectively the last few days, which he did,' Irwin said of Fleisher.
Fleisher ran his streak of consecutive rounds of par or better to 24. He also has recorded nine straight rounds in the 60s at the RJR Championship. The previous tournament record for scoring was 195, which was set by Irwin in 1997 and tied by Fred Gibson in 1999.
Larry Nelson, who won this event in 2000, carded a final-round 69 to finish 10 shots back. Nelson was joined by Mike McCullough and Ed Dougherty in a tie for fourth at 9-under-par 201.
Final results from the RJR Championship