Fleetwood went into the final round of the US Open at Shinnecock Hills, six shots off the pace, but he carded a stunning round of 63 to set a target in the clubhouse of two over par.
The Race to Dubai champion was impeccable in and around the green with his approaches at six and seven.
He also made an incredible 55-foot putt for a birdie at the second.
While Shinnecock Hills has proved very hard to tame this term, Fleetwood gave himself a chance of landing his first Major.
But the Englishman thinks his score will fall just short.
Speaking after his round, he said: “I feel quite normal. It’s a strange feeling when you’ve shot a 63 and feel disappointed.
“Overall though I’m very happy. I’ll have to just wait and see.
“Right now I feel like it’s just shy but you never know. The more you do it the more you get used to it.
“It’s what we practice for and I believe in myself. I had to trust the clubs and I wish I could go back and hit a couple of different putts.
“If you don’t enjoy those moments then there’s something wrong.
“You’ve got scoreboards all the way round so I knew what was going on. I was more interested in the 62.
“If I went back again I’d hit the same putt on 18. It was just so slow. I hit it left edge like I wanted to.
“I wanted that crowd to be really loud and memorable but it was still great.
“I’m going to have some lunch and a drink and sit with Finno and Claire and just wait. I’ll wait and see what’s happening and just hope.”