Fitzpatrick managed to play bogey-free on a sunbaked Copperhead course at Innisbrook that ruined the hopes of so many others, including overnight leader Sungjae Im.
The final hour on Sunday turned into a duel with Lipsky (70), the 37-year-old American who has won on four tours around the world but never on the PGA Tour.
Fitzpatrick, who missed four birdie chances from inside 10 feet in a seven-hole stretch around the turn, holed a 30-foot birdie putt on the par-3 15th to take the lead, only for Lipsky — playing in the group behind him — to make a seven-foot birdie on the 14th to catch him.
The Englishman, who won the DP World Tour Championship to close out the European tour season last November, had the final say. His birdie putt was pure and the 2022 US Open champion was emphatic thrusting his fist down to celebrate.
Lipsky's birdie chance from just outside 30 feet on the 18th just missed to the left.
Fitzpatrick's victory, his third on the PGA Tour to go along with nine European tour titles, came one week after he felt he did everything right only to see Cameron Young beat him on the final hole of The Players Championship.
"The big thing was I felt I was playing well," Fitzpatrick said.
"I wanted to continue that and felt like I had the confidence in myself to do so. To do that for four rounds was special this week."
Fitzpatrick finished at 11-under 273 and just ahead of Lipsky, who matched his best finish on the PGA Tour and moves to No.33 in the FedEx Cup standings.
Jordan Smith (66) of England finished third.
"Almost pulled it off," Lipsky said.
"It was close. Hats off to Matt."
Im (74) began the final round with a three-shot lead and that was gone quickly due to a putter that went cold on him. The South Korean, who had led since the opening round, didn't make his first birdie until the 11th hole.
Marco Penge (71), among five players tied for the lead at some point in the final round, fell back with bogeys on Nos.12 and 16 to join Im and Xander Schauffele (65) in a tie for fourth.
Karl Vilips, the only Australian to make the weekend cut, shot 73 to finish joint-64th at two over.
With AAP.
