'I had no doubt I could win again, but there are times when you doubt yourself,' Fleisher said. 'Hopefully, this will boost my confidence. I just need to make some putts.'
Fleisher earned a first-prize of $210,000 for his 12th career Senior Tour victory.
Hale Irwin, Walter Hall, Jose Maria Canizares, Doug Tewell and Vicente Fernandez tied for second place at 5-under-par.
Jerry McGee, who led after the second round, struggled to a 5-over 77 on Sunday and finished in a tie for eighth at 3-under-par. He made three bogeys and a double bogey on the back nine to fall out of contention and remain winless in 240 career Senior Tour starts.
Fleisher started two shots behind McGee, but took the lead for good with a birdie on the par-3 8th hole. He added a birdie at the 11th hole to reach 10-under-par, but suffered bogeys at 14 and 18.
Hall, who was 5-under at the start of the day, was 3-under for the round after a birdie at the 16th hole. He was one shot behind Fleisher at the time, then hit his tee shot at the par-3 17th into the water and took a triple bogey to fall out of contention.
Irwin, who won this title in 1997 and '98, shot a 2-under 70 for his share of second place, as did Canizares. Tewell, who won the Tradition last week, carded a 1-under 71 on Sunday and Fernandez, the 1999 winner here, shot an even-par 72.
Defending champion Larry Nelson finished alone in seventh place at 4-under-par.
Full-field scores from the Las Vegas Senior Classic