Molinari and Fleetwood became the first European pair to win all four of their matches together at Le Golf National in France.
British Open champion Molinari went on to compile a perfect 5-0 record, matching the feat of American player Larry Nelson, the only other player to do so under the current format.
The duo will be reunited in the first two rounds of this week's British Masters at Walton Heath, with Ryder Cup teammate Thorbjorn Olesen completing the marquee group, as Fleetwood seeks to close a gap of 1.4 million points to Molinari at the top of the Race to Dubai points list.
"It's going to be a little strange to try and beat each other instead of playing as a team," Molinari said. "Winning the Race to Dubai is the big goal I have, but there's Tommy and many other guys who are chasing me."
"This summer has been a bit of a blur," the 35-year-old Italian added. "It's been going fast with so many things happening and really not enough time to rest and recover.
"My back at the end of the Ryder Cup was not great. On Monday, I couldn't do my shoelaces. I'm not a kid like Tommy. I need to manage my energies and my body."
After this week, Molinari's only event before the season-ending DP World Tour Championship in Dubai will be the WGC-HSBC Champions event in China, while Fleetwood will compete in that event and also in the Turkish Airlines Open.
Fleetwood, 27, admits he is feeling "jaded" after a gruelling season as he tries to catch Molinari and win the Race to Dubai for a second year in succession.
"I might get nowhere near and it's a stretch as a goal to think about it, but I'd love to play Dubai with a chance," said the Englishman. "I'd love to get in contention in a couple of events and maybe win one."
Tournament host Justin Rose can return to the top of the world rankings with a top-two finish.
"Reaching world number one is an achievement and a milestone that is huge to me," he said. "Obviously I want to get back there as soon as possible and winning the British Masters as tournament host would be a great way to do that."