The Scot joined Kei Nishikori atop the John McEnroe group with a 6-3 6-2 victory -- his 20th win in a row -- to avenge a defeat to the Croatian in August at the Cincinnati Masters.
How Murray must have reveled in being introduced as the world No. 1 ahead of the clash in London, not far from his residence, after overtaking Novak Djokovic as No. 1 a week ago. He received a rousing reception and is clearly the crowd favorite at the event, given Roger Federer's absence.
But Murray hardly has time to sit back and enjoy his immense accomplishment, since the Serb is almost assured of regaining top spot if he wins the tournament -- and despite a recent slump, he is the four-time defending champion.
Perhaps the pressure of playing his first match when atop the rankings against a grand slam champion -- this was no easy first-rounder at a major -- plus fatigue accounted for Murray's noteworthy demeanor in the early going.
He appeared to complain to the chair umpire Damian Steiner about noise from the crowd during points, jawed at his support camp -- that, however, is nothing new -- and took over the allotted limit of time between points. In the seventh game he looked utterly spent.
Or perhaps not.
"I didn't feel any more nervous than usual," said Murray. "It's just quite different conditions in there than what we've been practicing in during the week. It's a lot slower than it has been."
After the 6-foot-6 Cilic missed his opportunities in the tense opener, often undone by his shaky forehand, Murray found things much simpler in the second set.
Murray went 4-for-5 on break points compared to Cilic's 1-for-5. Cilic's bright yellow shorts turned out to be louder than his game.
"When you start winning, you gain confidence," Murray told the crowd in an on-court interview. "In the important moments today, on the break points, I was a little more solid than Marin.
"He had some chances in the first set and the beginning of the second set. When I had my opportunities I took them. That's what winning matches does for you.
"It was a great atmosphere.
"I'll try and keep going until the end of the year now."
His next challenge comes from Nishikori, one of only two players to beat Murray since the start of September. It was the Japanese baseliner who upset the three-time grand slam winner in five sets in New York.
Cilic claimed his first Masters title by downing Murray in Ohio and carved out two break points Monday in the first game. A good second serve from Murray saved one, while an errant Cilic forehand accounted for the other.
Three breaks of serve ensued, with Murray saving a break point at 3-1 with an ace.
Cilic gathered momentum on his serve from late in the first set to 2-1 in the second -- Murray had fended off another break point at 0-1 with an ace -- yet didn't win another game.
It led Murray, who has never made the final at the tournament, to proclaim: "It's one of the best matches that I've played here over the years."
Earlier Monday, Nishikori toppled another three-time grand slam winner, Stan Wawrinka, 6-2 6-3.
Djokovic seeks to improve to 2-0 in the Ivan Lendl group -- Lendl is one of Murray's coaches and has been influential -- when he plays Wimbledon finalist Milos Raonic on Tuesday.