Irwin had four birdies on Nos. 10-14, but closed with four consecutive pars to finish at 9-under 204, one shot behind Tewell.
Fleisher, trailing by one shot after Tewell bogeyed the par-4 No. 18, hit his second shot into the water on 18 and made double-bogey 6. His 4-over 75 tied Dave Stockton at 206.
Tewell, who shot 2-under 69, won $225,000 for his fifth victory on the senior tour, one more than he had in nearly 25 years on the PGA Tour. He was the only player in the field to shoot three rounds in the 60s on the 6,783-yard course at the Tournament Players Club of Tampa Bay.
'It feels good,' said Tewell, who started the round three shots behind Fleisher. 'I've been on myself pretty hard after the first three events because I thought I'd played pretty well, but just haven't putted very well.
'But after making that 50-footer (for birdie) on the first hole, I started thinking this just might be my day.'
Tewell made birdie putts at 5 and 6, and took a one-shot lead over Tom Kite by two-putting from 40 feet for birdie on the par-5 seventh. Tewell maintained the one-shot lead over Kite with the 18-footer at No. 12.
'That putt was huge,' Tewell said. 'To knock it in from off the green, I could have knocked that thing 6 or 7 feet by the hole coming off that hill.
'I have to kind of give Dana Quigley an assist. The ball rolled over his coin and it kind of veered it back into the left edge of the cup. Those are the kinds of things that happen when you win.'
Kite, who started the round one shot behind Fleisher, hit into the water at Nos. 12 and 14, making double-bogey on each hole. He finished at 6-under 207.
Tewell's bogeys at 16 and 18 were only his second and third of the tournament.
'It wasn't a textbook finishing round, but under the circumstances, this course can be tough coming down the stretch,' Tewell said. 'I feel very fortunate.'
Fleisher hit a 3-iron from 195 yards in his approach on No. 18. It went right before catching the water.
'Pretty ugly, pretty ugly,' Fleisher said. 'I never felt comfortable all day. ... I hit the ball very poorly. I've got no excuses.'
Irwin had six birdies, including a 30-foot pitch from just off the green on the par-4 fifth.
'I had a nice run on the back side,' Irwin said. 'I just couldn't get it close enough.'
Tewell dedicated the victory to family friend Brooke Burress, who died in an auto accident in December.
Tewell, picking up 225 points, moved into fourth place in the Charles Schwab Cup race. Kite leads with 388 points. John Jacobs is second at 372, and Irwin third with 357. The season-long race culminates with the winner receiving a tax-deferred $1 million annuity.
Terry Dill was disqualified after his round for signing an incorrect scorecard. Dill signed for a four at No. 15, but had a five.
Full-field scores from the Verizon Classic