"I feel like a 20-year-old and the way I'm playing, it's great," the 31-year-old Spaniard, who made it to the semi-finals in 1998, said after his fourth-round victory.
"When you're the oldest guy in the draw you get a lot of support from the crowd and it's a great feeling to be in the quarters," he added.
The Spanish 17th seed was pushed hard by 19-year-old Gulbis but came through to set up a clash with third seed Novak Djokovic of Serbia or Argentine 23rd seed Juan Monaco.
"These kind of matches, they're the ones that keep me very motivated," said Moya, who went five sets to defeat 23-year-old German Philipp Kohlschreiber in the third round.
"The match I won the other day against Kohlschreiber, it's amazing. You're so happy when you finish that kind of a match."
Moya has enjoyed a resurgence this year.
After finishing 2006 ranked 43rd, the Spaniard is now ranked 17th after reaching the quarter-finals at the French Open and winning his 20th career Tour title at the Croatian Open.
The 1998 French Open champion, runner-up at the Australian Open 10 years ago, said he was having too much fun to consider retirement.
"I have never been close to retiring, to be honest," Moya said. "People were asking me, but I didn't feel that it was my time yet. Probably if this year was like the last couple of years, maybe you start thinking about it.
"If I stay healthy, if I'm playing at this level, I can't find a reason to retire. I'm enjoying it as I never did before."