It meant he moved back into pole position at half-way after his nearest contender, fellow Englishman Justin Rose, who had moved ahead of him in the projected rankings after the first round, slipped behind again by bogeying the last hole.
Yet the battle for the $1.25 million (£947,310) season-long accolade remains almost too tight to call. Rose's second round 70 leaves him still two shots ahead of 11th placed Fleetwood, but that final hole slip dropped him to joint third in the tournament.
The in-form Rose, who trails Fleetwood by 256,737 points in the race but has won his last two tournaments, needs to finish in the top two in Dubai and beat his compatriot to triumph.
The half-way pacesetter was another Englishman, Matthew Fitzpatrick, the defending DP World Tour champion who shot a second straight 67 to move on to 10-under, one clear of compatriot Tyrrell Hatton, who recorded a blistering day's best 63.
Fleetwood was delighted to get back on track to take the big prize.
"There's still a tournament to play for and there's still a Race to Dubai to play for. But I needed a low one today for sort of both purposes," Fleetwood said.
"So the sole focus was to try to get back into this event today. I knew I needed a low one."
Masters champion Sergio Garcia, the only other contender in the Race, is a shot behind Fleetwood and three adrift of Rose after his 69.
(Reporting by Ian Chadband; Editing by Toby Davis)
