There was a match-play feel to the action in the final group on Friday as a fast start saw Hatton open up a three-shot lead before fellow first-round co-leader Fitzpatrick reined him in.
Yorkshireman Fitzpatrick briefly claimed the outright lead in the closing stages courtesy of a late birdie blitz but Hatton took advantage of the short 17th to regain a share of first place.
There was late drama at the 18th as a pair of disappointing tee-shots left the co-leaders with decisions to make.
Hatton opted to take a drop after finding his ball plugged in the penalty area and produced an excellent recovery shot to give himself an outside birdie chance, but ultimately had to settle for par and a round of 67.
Fitzpatrick, meanwhile, played his second shot from among the trees and walked away with no damage done to sit alongside Hatton on 12 under par.
Fitzpatrick, who went into this week's season finale third on the DP World Tour Rankings in Partnership with Rolex, leads the projected standings ahead of Rory McIlroy and Ryan Fox with 36 holes remaining.
Swede Alex Noren and Spaniard Adri Arnaus head into the weekend in a tie for third, three shots behind the co-leaders on nine under.
Jon Rahm, who like Fitzpatrick has a stunning record at Jumeirah Golf Estates' Earth Course, sits alongside fellow Spaniard Jorge Campillo one shot further back in a share of fifth.
Fitzpatrick was delighted with his second-round performance, saying: "Really, really pleased with the way I played again. And yeah, scored really well too. It was a good day.
"Just got to keep pushing on, just keep playing how I feel like I'm playing right now. I feel really comfortable with where my game is at, particularly after three weeks off, and looking forward to the weekend.
"I feel like I've played two good rounds to start with and put myself in position and I'll just keep doing more of the same and see where it gets me come Sunday."
Hatton said: "I'm pretty happy with the score. I got off to another nice start again today.
"I feel like I've generally played some pretty good golf. We got a little unlucky on the back nine, which I feel like it stalled our momentum a little bit.
"Really happy to par the last today. That's probably one of the best 3-woods I've hit in my life, to be fair, and I didn't realise it was as close as it was. It was a tough crowd on 18! Nice way to finish the day.
"Hopefully the putter stays fairly hot and we have a good weekend.
"There's still 36 holes to play. I have a fairly good record around here. Matt has an excellent record around here. But you know, we'll enjoy each other's company tomorrow and hopefully we can keep playing well."
Rory McIlroy hopes his stunning finish to round two at the 2022 DP World Tour Championship is the trigger to make "something happen" over the final 36 holes.
McIlroy went into the final event of the season leading the DP World Tour Rankings in Partnership with Rolex but an opening 71 and a pedestrian start to his second round opened the door for Matt Fitzpatrick to potentially pip him in the final standings.
Needing a big finish to give himself hope, McIlroy birdied the 16th from six feet and the island 17th from ten before saving his best for last.
A breathtaking 226-yard uphill approach to the 18th green settled three feet from the hole and he nervelessly holed the putt for eagle, a 68 and a five-under-par halfway total.
Asked if it changed his mindset going into the weekend, McIlroy said: “Yeah, 100 per cent.
“Pretty mediocre golf for the first 33 holes and then something sort of clicked. Whatever it is, I need to bottle it for the weekend.
“It was nice to finish with a flourish there and put myself a little closer to the guys.
“You never know, that finish here on Friday could be key to something that happens over the next 36 holes.”
Regarding his dream shot into the final green, McIlroy said: “I think it was playing 233 (yards) adjusted with the elevation, it was just a perfect number for a four iron.
"The TV tower was a great line, I knew I just needed to make a good solid swing and yeah, that was a really good golf swing. More of those needed over the weekend.
"You make your score over 72 holes, but you’re going to have little spurts like the last three holes that I just had, where you play them in four under, or you play nine holes in five under. It’s just waiting for that to happen and not forcing the issue.
“I felt like I started forcing the issue on 14 and 15 today, played those two holes in one over which wasn’t great. Re-setting for the last three holes, my goal was to play them in two under and I played them in four under, which was really nice.”
Ryan Fox has had a slow start T37 73 72 +1.
