Lee Westwood is one back after dropping his only shot of the day at the last.
Order of Merit leader Henrik Stenson and second placed Danny Willett are tied for 17th on three under.
Rory McIlroy, bidding to win the European Tour's season finale in Dubai for a third time, posted six birdies in a 68 but is eight shots adrift.
The Northern Irishman, who has never finished worse than 11th in seven appearances at Jumeirah Golf Estates, had opened with a three-over 75, his first over-par score in the event.
"Yesterday was just one of those days. I was mentally very flat, still in holiday mode, and not quite switched on to what I needed to do," he said.
"If can keep improving each and every day, then I might not be too far away at the end of the week."
The Tour Championship is the final event of the Race to Dubai, with four players still in with a chance of topping the money list.
Open champion Stenson, who won this tournament with a course-record 25 under total at the Earth Course in 2013, leads by 299,675 points but Masters champion Willett can leapfrog the Swede should he win the tournament.
Willett would also top the list if he finishes second and neither Stenson nor Alex Noren win in Dubai.
Noren, another Swede, needs to finish at least second and hope Stenson and Willett finish down the field and he is five strokes off the lead after a round of 69.
Stenson, the 2013 Race to Dubai winner, was more concerned with the well-being of a female spectator hit on the head by his tee shot on the 13th.
"I had some reports later in the round that she was doing OK. I'm just making sure that we're going to get her details so I can send her something nice," he said.
McIlroy, who has won the Race to Dubai for the last two years, has an outside chance which requires several permutations falling into place - including Stenson finishing no higher than 46th in the 60-man field.
Sergio Garcia and Francesco Molinari both carded five-under 67s to share the lead at nine under at the halfway stage of the DP World Tour Championship.