The Englishman made seven birdies with just one dropped shot as he carded a 66 that moved him to nine under in perfect conditions on day three at St Andrews.
He has finished second in two Majors before but in very different circumstances and believes both of those experiences could stand him in good stead.
In 2018, he carded a closing 63 to fly up the leaderboard and finish second at the U.S. Open Championship, while in 2019 at this event he went out in the final group at Royal Portrush as he finished second to Shane Lowry.
I’d love to be in with a chance coming down the back nine tomorrow but it is very special to still be in and amongst it
"I think my experience of playing on a Sunday, I didn't win or anything, but I felt like I did a pretty good job with Shane aside," he said. "Shane was exceptional on that particular day.
"The more you're up there on a Sunday and compete, the more you have a chance of eventually getting over the line. I think that's all you can really keep doing and keep focusing on.
"It's nice to be playing well again. Portrush feels like a long time ago at the moment but at the moment and in the current situation, I feel like I've been gradually improving, gradually building a bit of momentum, and results have been slowly coming.
"My game's been holding up much better throughout four rounds than it was during last year where I was nowhere to be seen in a way. So it's nice to be sort of having a go again and seeing what we can do.
"There is a low score out here. It is obviously not in my hands at the moment. All I can do is try to stick in.
“I’d love to be in with a chance coming down the back nine tomorrow but it is very special to still be in and amongst it."
At Shinnecock Hills Golf Club four years ago, the winning total was one over par and Fleetwood insists he enjoys the tough challenge of golf's biggest four events.
"I enjoy Majors," he said. "I enjoy preparing for them. I think in general the tougher tests tend to fit my game. I'm a bit more of a patient player. I don't know why but it brings out the best in me in a way.
"It's nice, a stat that I've shot a lot of good rounds in Majors and you draw on those kinds of things to give you confidence. I've always liked playing these events. I've always liked testing myself against the best players on the toughest courses.
"I haven't won a Major yet and, to be honest, I haven't won any kind of tournament for a while and my game hasn't really been in a position to do so. But it's coming back."