Molinari enjoyed a share of the lead after 14 holes of the first round at Jumeirah Golf Estates, only to three-putt both the 15th and 18th to card a four-under-par 68 and finish two shots behind joint leaders Jordan Smith and Adrian Otaegui.
And with playing partner, Ryder Cup team-mate and Race to Dubai rival Tommy Fleetwood making an unlikely birdie on the last from off the green, the reigning European No 1 was just a shot behind following a battling 69.
“It’s a shame because I putted really well up until the 14th and then I just misjudged the pace on a couple of those putts and left myself more work to do than I needed to,” said Open champion Molinari, who would be the first Italian to top the money list.
“My game was OK, probably not my best, but putting and short game was very good up until the 14th, and that’s how I built the six-under score to that point.
“It’s only Thursday so there are so many things that can happen. Both of us did not hit the ball our best but we managed to scramble well and close out two decent rounds.
“I did a good job of thinking shot by shot and that’s what I need to do. I don’t think there is any benefit to thinking about what-ifs. It’s too early.”
Fleetwood, who has to win and hope Molinari finishes outside the top five to retain his title, admitted he had to work hard to keep his round together on the back nine, but added: “Sometimes those are the rounds that maybe win you golf tournaments at the end of the week.
Former Masters champion Danny Willett set the early clubhouse target.
Sheffield’s Willett, 31, who has not won since claiming his maiden major title at Augusta in 2016, carded seven birdies and two bogeys in a five-under-par 67 that left him one off the pace.
“It’s a shame it’s the last event of the season,” said Willett. “From June, July onwards we were making better strides and we could work harder and work longer and that’s had a big impact.
“Now we’re on track and we’re able to work a bit harder and I’m seeing the results quite nicely in practise and in Turkey it was nice to kind of take it to the golf course.
“We got here and have the ball under nice control and the movement is pretty good. We’ve got 54 holes left in the year and will just play till the bell goes and see where we finish.”