After two rounds, a familiar face topped the leaderboard in the $8 million (6.78 million euro) event. Matthew Fitzpatrick, the defending champion, hit a second 67 to finish 10 under par.
But much of the focus in the European tour's season-ending event was on the two men leading the "Race to Dubai". Fleetwood, who struggled in the first round, shot a seven-under-par 65 in the second to make up five shots on Rose, who hit 70. Rose is tied for third, two shots ahead of Fleetwood who is in a four-way tie for 11th.
For Fitzpatrick, Friday was eerily similar to the final round last year when he won with a birdie on the 18th as Tyrrell Hatton made a bogey.
This time, Fitzpatrick sank a 25-footer on the final hole on the Earth course at Jumeirah Golf Estates, while Hatton, 10-under through 17 holes, dropped a shot on the 18th from a horrible lie in the bunker to finish on nine-under par.
Rose can claim his second European end-of-season title by finishing first or solo second if Fleetwood does not win, or with a top-five showing if his younger compatriot finishes down the leaderboard. Fleetwood leads the race by 256,737 points.
"It's all about how you react to stuff, isn't it?" Fleetwood said after a birdie finish. "Yesterday, I was really unhappy with how I reacted early on. Got off to a bad start and got back into it and I didn't really play great.
"I was on the putting green till dark last night. Today was just a much better day. And I am happy I still have things in my hand instead of being way back."
Rose, who played another solid round with four birdies in increasingly difficult conditions, was disappointed with his three-putt bogey on the 18th.
"Slightly frustrating round," Rose said. "There were probably a lot of chances I could have taken. But at the same time, it's a good mark. It's a good, solid effort after yesterday and puts me in great position for the weekend."
The only other player in contention, Masters champion Sergio Garcia, added a 69 to his opening-round 70 and is one shot behind Fleetwood.
Rookie Julian Suri (68) of the USA and Kiradech Aphibarnrat (67) of Thailand were in tied third place at eight-under par 136 alongside Rose.