In an earlier match at the O2 Arena on Monday (Nov 14), fifth seed Kei Nishikori shocked world No.3 Stan Wawrinka of Switzerland 6-2, 6-3, reports Xinhua.
Murray added 200 points with his 12th win over Cilic and now has 11,110 points in the world rankings as he battles Novak Djokovic (10,980 points) for year-end No.1.
Enjoying a career-best year, Murray is now 73-9 with eight titles overall and has extended his winning streak to 20 matches since Sept. 20.
He will next play Nishikori on Wednesday (Nov 16).
Murray broke twice to take a 3-1 lead while Cilic, who committed 17 unforced errors, looked for a second break, but Murray was able to clinch the 46-minute opener.
In the second set, Murray broke twice in a run of five straight games to wrap up victory in 90 minutes.
"A big thank you for all of the support, it was an incredible atmosphere today," Murray said after the match. "I really appreciate it."
Nishikori, who is playing the year-end finale for the third straight year, needed only 67 minutes to prevail. It is the Japanese star's third victory over Wawrinka in seven meetings.
"I felt very comfortable out there," Nishikori said.
"He wasn't playing his best. He made a lot of unforced errors. I see a lot of opportunities today."
Wawrinka, the oldest player in the field at the age of 31, did not create any break point opportunities.
"It was not a great match, compared to what I [know I] can do," he said.
"It wasn't a great day for myself. In general, I think he played well and put a lot of pressure from the beginning. I don't think I found anything on the court today. I was a little bit slow on everything. I was hesitating a lot with my game [and] my movement."