It was Cilic’s defeat of Novak Djokovic at the Paris Masters that opened the door for Murray to seize the number one ranking he had spent his whole career pursuing.
Murray repaid the favour with a 6-3 6-2 win, his 20th in succession, although it was far from a drubbing as Cilic tried his utmost to ruin the Scot’s homecoming.
Four more performances like that at the O2 Arena this week should guarantee the 29-year-old will end 2016 leading the pack.
Murray had lost his most recent meeting with Cilic, the Cincinnati Masters final in August, and on Wednesday he will face Japan’s Kei Nishikori who stopped him in the US Open quarter-finals, Murray’s last Tour level defeat.
Nishikori had earlier beaten Swiss Stan Wawrinka 6-2 6-3 in the John McEnroe group, although that match was as one-sided as the scoreline suggested with Wawrinka badly off key.
Murray has been handed a tougher-looking group than Novak Djokovic, the man he deposed and who could still snatch back the top ranking, but he cleared the first hurdle in style in front of a near full house who welcomed him home like a returning hero.
“It was a great reception,” Murray, Britain’s first ATP singles world number one, told reporters.
“After a long kind of few months, it’s nice to know that I’m going to be finishing the year playing in that sort of atmosphere. It helps you get up for the matches a bit more.”
Murray served four double faults in the early stages and came under a fierce assault by Cilic.
