The 36-year-old can only be denied the overall crown if Fleetwood wins the final of the season and he finishes worse than the fifth one with another.
Molinari was the leader behind Jordan Smith and Adrian Otaegui on four.
Danny Willett of England is in 5th place under the spanish leader Jon Rahm.
Molinari kept a 14-hole lead at the Jumeirah Golf Estates, but then had three hits on the 15th and 18th.
Italy, Fleetwood’s playmaker, said: “It’s only Thursday, so a lot of things can happen, but we did not do the best we could but we managed well and finished two rounds.
“I did a good job thinking about shooting with a shot and that’s what I needed to do.I do not think there is any benefit to thinking about what-ifs.
Fleetwood, who has a Molinari partnership at the Ryder Cup called “Moliwood,” added: “You are still in this week’s Race to Dubai – a round and we have a chance. Our on the water for that, we will be happy and continue. ”
The big winner four times Rory McIlroy and Masters champion Patrick Reed are part of a 12-way tie on three under one day when 46 of the 60 men field a horizontal shot or better.