The 69-minute victory crowned a magnificent week for the 29-year-old English No.1 and British Champion, who was kept on court for more than two hours in his semi-final battle with compatriot James Willstrop the previous evening.
Matthew showed few signs of fatigue following one of the most epic battles in squash history and it was Gaultier who blamed tiredness for letting slip a 6-2 lead in the third game.
The Frenchman was still ahead at 9-6 but was unable to convert that lead as Matthew forced the second tie-break of the match, finally clinching it 13-11 after the 27-year-old from Aix-en-Provence held game ball at 11-10.
Matthew then ran out an easy winner in the final game as Gaultier’s challenge wilted.
Earlier, Matthew had won the crucial opening game 12-10, despite Gaultier holding game ball at 10-9.
The Frenchman, who topped the PSA World Rankings in November, responded in stunning style, racing to a 5-0 lead and winning the game comfortably by a five-point margin.
Gaultier continued the attack in the third game but was unable to maintain his control as Matthew mounted a phenomenal physical response to clinch the title 12-10, 6-11, 13-11, 11-3 and continue his quest for the converted World No.1 ranking.
"It's a bit of a miracle I pitched up today," said a jubilant Matthew after his third successive PSA World Tour title success this year and his 13th undefeated match in a row. "Lots of thanks to Sylvan (Richardson) - a 20-minute session today turned into two hours as he found one sore point, then another, then another and fixed them all up!
"I got a bit lucky today - Greg could easily have won 3/0 but I won some big points at the crucial stages.
"If there's two tie-breaks in a match, you sort of expect them to go one each. I was feeling and playing better at the end and it may have been preying on his mind that he could have won 3/0," concluded Matthew, who now has 13 PSA World Tour titles to his name.
The dejected runner-up was full of praise for Matthew: "Congratulations to Nick, I was a bit unlucky to miss out on game balls in the first and third, but he stuck in well - and he's big too!" Gaultier added.
Issued by isportgroup.com/SquashNews
internationalSPORTgroup would like to thank Howard Harding, PSA World Media Manager, for his contribution to this release.