They all posted a three-under 68 to peg a crucial foothold after a hectic first day in Northern Ireland.
While Hatton was happy to nudge closer towards a feel-good factor after a post-Ryder Cup slump, Fleetwood revealed the secret to his bogey-free round was easing the self-imposed stress.
“It’s been a bit of a come-down after the Ryder Cup and it’s fair to say that I have struggled this year,” said Hatton, who starred in Europe’s victory over the USA in Paris in September 2018.
“But my game feels in a good place, and hopefully I can keep playing well and that will lift my spirits.
“It’s pretty special, this is my eighth Open so I’ve got a bit of experience there. The crowds here are great.”
Fleetwood eased around Northern Ireland’s testing north coast course, completing a serene and error-free round where others battled through wind, rain and personal frustrations. The 28-year-old admitted he shook off the personal pressure to avoid dropping any shots, in a very tidy first-round performance.
“Any time you’re going to go bogey free at a major, take it and run,” said Fleetwood.
“I played really consistently, so I’m just happy with that.
“I conducted the round very well today so I’m pleased. I hit it well, I was very consistent, I was always in play, pretty much. And that’s obviously vital.
The 46-year-old Westwood, playing in his 25th consecutive Open, has had one runners-up finish, two thirds and a fourth but has not finished in the top 20 in his last five outings at the event.
“It was nice to shoot a low score the first round of the tournament and get right in there. You just take it one day at a time, obviously,” he said.
“I’ve seen all this before. I’m just out there enjoying myself.”
Justin Rose kept himself in the hunt for glory with a steady two under, along with Ashton Turner.
“Today was a good day of links golf,” said Rose. “For me the wind today was a perfect amount on a links course.”