Fleetwood has been highly impressive over the past few months, winning his maiden PGA title at the Tour Championship in August before helping Europe beat the United States in the Ryder Cup in September.
Last month. the world number five claimed a first DP World Tour title of the season in India.
“I am playing very good golf at the moment and I have found myself in this position a lot throughout the summer, but I never take it for granted,” Fleetwood told the DP World Tour website.
“This is what you practise for, these are the times of our lives and I am enjoying it very much.”
Spain’s Nacho Elvira, who posted a 65, is two shots off the lead, while Englishman Andy Sullivan and New Zealander Daniel Hillier are tied for fourth on 17 under.
Rory McIlroy finished the day six shots off the pace following his round of 66, which kept him in pole position to win a seventh Race to Dubai title as the season’s best golfer on the DP World Tour.
The Abu Dhabi Championship is the first of two DP World Tour end-of-season play-off events, with the top 70 players competing this week and the leading 50 advancing to next week’s finale in Dubai.
With a total of 9,000 points to be shared among the field this week (1,500 to the winner) and 12,000 more next week (2,000 to the winner), the Harry Vardon Trophy for the season title is up for grabs.
Northern Irishman McIlroy, who is two behind Colin Montgomerie’s record of eight years as the tour’s number one, leads the Race to Dubai standings by just under 500 points from Marco Penge, the Englishman who has won three times on tour this year.
Penge sits on 11 under for this week’s tournament after his 70 on Saturday, finishing with a damaging double bogey after finding water on the par-five 18th.
Fleetwood is almost 2,800 points adrift of McIlroy in the Race to Dubai standings so to have any chance of a highly unlikely overall victory would need to win both play-off events and hope his Ryder Cup team-mate falters.