Fitzpatrick birdied the first five holes on his way to a front nine of 30 and a flawless opening 65, joining Hatton on seven under par after his Ryder Cup team-mate had dropped his only shot of the day on the 18th.
With leader Rory McIlroy and second-placed Ryan Fox shooting 71 and 73 respectively, Fitzpatrick is now projected to finish top of the DP World Tour rankings for the first time.
"I was laughing to be honest," Fitzpatrick, who was suffering from a sore throat, said of his flying start.
"I literally said to Billy (Foster, his caddie) yesterday, when we won in 2020, didn't we have four in a row? And then we did four in a row and laughed about that and I made a fifth. It was a nice start to the day.
"I think the biggest thing I'm pleased about today is just hitting 17 greens and the one I missed, I was a complete idiot. That was the big thing that I was happy about today is that I kept giving myself chances and putted well as well."
Hatton was annoyed to bogey the 18th after finding a fairway bunker off the tee and needs to win the season-ending event to extend his run of at least one victory a year to four.
"Obviously it was a good day," the world number 29 said. "I hit a lot of good shots, putter was great. I'm kind of happy with that start although my head's a bit fried at the moment. My mind is just raging at the last there. But it is what it is."
Asked to sum up his season, Hatton added: "I would say consistently very, very average. Apart from that good finish at Bay Hill (joint second) I think we were leading the Desert Classic on Saturday afternoon so there was a few good events at the start of the year I guess.
"But after Bay Hill it's been pretty boring. Nothing to get excited about to be honest."
McIlroy began the week with a 128-point lead over Fox and covered the first eight holes in three under par, but the two-time winner then bogeyed the ninth, 12th and 16th before making a welcome birdie on the last.
"Yeah, certainly not what I was hoping for," the world number one said. "Three under through eight holes, a solid start with some chances coming up and just started to drive the ball a little crooked on the back nine.
"Made that bogey on 12 and didn't birdie 14 or 15, and then an unforced error with the three-putt on 16, so it was nice to birdie the last just to shoot under par.
"Obviously I've had three weeks off since the CJ Cup, so I'm trying to knock the rust off a little bit there. There was enough good stuff in there. I made five birdies and hit some decent shots, just need to be a little tidier tomorrow."
Sweden's Alex Noren lies a shot off the lead after a back nine of 31 in his 66, with Nedbank Golf Challenge winner Tommy Fleetwood part of a five-strong group on four under.