World number one Gaultier faced Matthew for the 36th time on the PSA tour in his quarter-final match at Vanderbilt Hall, inside the iconic Grand Central Terminal.

The 35-year-old looked to be on the ropes during the first game of the 92-minute match, losing 14-12 to three-time Commonwealth Games medallist Matthew, who was appearing at the tournament for the final time in his career.

Gaultier, however, swung the momentum back his way by winning the second game comfortably by an 11-6 scoreline before pinching the third 12-10, putting him in the lead for the first time in the match and giving him the platform to take the fourth and final game 11-7.

Combined Age = 7️⃣2️⃣
Squash level = ??

Simply stunning squash from @nickmatthew and @GregoryGAULTIER in New York ?? #Legends pic.twitter.com/zqpURQauKJ

— PSA World Tour (@PSAWorldTour) January 23, 2018

After his win, Gaultier said: "We've been playing each other for 20 years, since we were kids, and he definitely made it tough today.

"He was dominating the centre of the court with his accuracy and made it very hard for me, he was hurting me on there.

"I just tried to dig in and retrieve as much as I could to keep the rallies going and make him work as hard as possible.

"We both gave everything.

"Of course, we are rivals, but we are friends as well and have a huge respect for each other.

"Playing here in this atmosphere is amazing and we both emptied the tank - hopefully I can recover well for my next round match now."

Gaultier will now face Germany's Simon Rösner, who defeated Nicolas Mueller 3-1 in his quarter-final.

There was more success for French players in the women's draw with number three seed Camille Serme, who became the first-ever French woman to win the tournament last year, coming out on top against Donna Urquhart of Australia 3-2 despite being 2-1 down earlier on in the match.

Serme's spirit was personified by her comeback in the fourth game when she recovered from 4-1 to win 11-6 before holding her nerve to take the match-winning game in the fifth by an 11-8 scoreline.

"When you are losing, you start thinking about not playing again and being out of the tournament, so that's when you fight even more," Serme said after her win.

"You think that you have nothing left to lose and that's when you relax a bit.

"I got a lucky bounce at the end and I just fought as hard as I could.

"She [Urquhart] made me struggle a lot so I'm happy to be through."

Serme will now come up against eight-time Commonwealth Games champion Nicol David of Malaysia in the quarter-finals.

David saw off Joelle King of New Zealand in her second round match.

Elsewhere in the women's draw, world number one Nour El Sherbini of Egypt defeated compatriot Mariam Metwally 3-1 whilst fellow Egyptian and number two seed Raneem El Welily struggled to get past 15th seed Tesni Evans of Wales, eventually winning 3-2 in 67 minutes.

El Sherbini will now face England's Sarah-Jane Perry in her quarter-final with El Welily facing compatriot Nour El Tayeb.