He shared the 54-hole scoring mark with Jim Colbert and George Archer, which they set in 1992, and Bruce Fleisher, who tied it in 2000. McNulty becomes the 11th man to win in his Champions Tour debut. The last to do so was Bobby Wadkins at the 2001 Long Island Classic.
Larry Nelson put pressure on down the stretch, including a birdie at the last, as he closed with a 68 to finish at 12-under-par 201.
The story for most of the day was Fuzzy Zoeller. He began the day at minus-1, but reeled off seven straight birdies en route to a 10-under 61, to tie Rocky Thompson's course record.
Zoeller finished at 11-under-par 202 and was joined in third by Tom Purtzer, who carded a final-round, 3-under 68.
McNulty, the overnight leader, opened with a birdie at the second to extend his early lead to two strokes. He came back with a birdie on the fourth at TPC of Tampa Bay to move three ahead of the field.
The Zimbabwe native stumbled to a bogey on the par-4 fifth and his lead fell to one stroke. Zoeller, in the midst of his birdie run, tied McNulty atop the leaderboard briefly when he birdied the 13th.
McNulty quickly answered with a birdie on No. 7 to regain first place at minus-12. He faltered to a bogey at the following hole, to drop into a three-way tie for the lead with Zoeller and Nelson.
Zoeller notched his final birdie of the day at the 14th to take over the lead outright at 12 under. He would later bogey the closing hole to drop back to minus-11.
McNulty birdied the 12th to regain first place as Zoeller faltered late. McNulty parred the next two holes and was caught on No. 14 by D.A. Weibring, who birdied the same hole.
Weibring, playing ahead of McNulty, fell off the pace with a bogey at the next, while McNulty took control. He chipped in for birdie at the par-5 14th and saved par from a bunker on the 15th.
McNulty, who was the medalist at the 2003 Champions Tour Qualifying Tournament, rolled home a 35-footer for birdie at the 16th to move three clear of the field.
'I really focused hard on that putt,' said McNulty of his putt at the 16th. 'I picked out a fine tooth pick to aim at and that's what I hit. I was delighted when it went in. That gave me the cushion I thought I needed to get to the house with.'
McNulty missed the fairway left off the 18th tee and laid up. He pitched his third onto the green and two-putted for bogey and the win.
'I couldn't control what Fuzzy was doing, so you just have to go out and do your own business,' said McNulty, who picked up $241,000 for the win. 'I had a couple of good things happen down the stretch when I needed them to happen. It's great to win.'
Zoeller was hot over his first 14 holes but cooled down the stretch. He birdied the first to get started, then ran off seven straight birdies from the fourth move to 9 under, three behind McNulty.
He continued his torrid pace with three consecutive birdies from the 12th to move into the lead. Needing one more birdie to become the first man on the Champions Tour to shoot 59, Zoeller cooled.
He collected three pars in a row to head to the closing hole needing birdie for 59. Zoeller missed the green right and tried to putt from a bad lie in the fringe. The ball came out soft and stopped some 10 feet from the hole. His par try slid by the edge as he closed with a 61.
'I birdied the first, then hit a couple other shots close and got on a roll. You know how this crazy game is,' said Zoeller, who won the season-opening MasterCard Championship. 'We just got into the flow with everyone making birdies. I hit the ball pretty close, made a couple of 10-footers for birdie and the ball just went in the hole. What can I tell you.'
Nelson shared second place to begin Sunday's final round. He birdied the sixth and eighth to grab a brief share of the lead. He continued his steady play as he notched nine straight pars to remain near the top of the leaderboard. As McNulty struggled on No. 18, Nelson put some pressure on as he birdied the hole, but McNulty bogeyed the hole to hold on for the win.
Weibring began the day tied for second. He managed a 1-under 70 to finish at 10-under-par 203 and alone in fifth place. Tom Jenkins also shot a closing 70 to come in sixth at minus-9.
Jim Thorpe, who carded a 3-under 68, shared seventh place with Gil Morgan (70), John Bland (69) and Vicente Fernandez (71) at 8-under-par 205.
Bruce Fleisher, the 2003 champion, closed with a 6-under 65 to join Tom Kite (69) at minus-7.