The progress of the players from Great Britain and Northern Ireland had been rather underwhelming, but 33-year-old Fleetwood remained patient and was rewarded with a top-10 finish.
In reality, Fleetwood needed a better round to put himself into serious contention but played solidly to leave him feeling optimistic going into next month’s US PGA Championship at Valhalla.
“I guess I needed a few more fireworks. But the golf course wasn’t giving much away,” said Fleetwood, who made his eighth appearance at the Masters.
“Who knows if my time will ever come, but all I can do is keep trying to put myself there and having performances like this.”
Northern Ireland’s Rory McIlroy was unable to finish with a flurry as his 10-year wait for the major title which evades him continued.
The 34-year-old won four majors between 2011 and 2014 – twice at the PGA Championship, plus the Open Championship and US Open – but was never in contention as he looked to become only the sixth man to complete the career grand slam.
McIlroy struggled in the testing conditions as he opened with rounds of 71, 77 and 71, carding a final 73 to finish well adrift at four over.
“It hasn’t been my year but I’ll keep coming back until it is my year,” he said.
England’s Tyrrell Hatton was level par after a final-day 69, while Matt Fitzpatrick ended four over and 2016 champion Danny Willett, playing in his first tournament since having shoulder surgery in September, faded from a good start to finish nine over.