The world's top two players met for a one-off match after competing in Shanghai and Kuala Lumpur over the weekend. McIlroy had been runner-up to his Ryder Cup team-mate Peter Hanson at the BMW Masters and Woods was fourth behind his fellow American Nick Watney in the CIMB Classic.
Three weeks after Woods defeated the 23-year-old by six strokes at the World Golf Finals in Turkey, it was McIlroy who had the edge this time. He had two early birdies and turned two in front before Woods chipped in at the short 12th, but the American bogeyed two holes later and could not get back on terms.
Neither player is staying on in the country for this week's WGC-HSBC Champions at Mission Hills.
McIlroy, who is flying to Bulgaria to watch his tennis-player girlfriend Caroline Wozniacki in action, next plays at the Singapore Open next week, while Woods has one event left in 2012, the World Challenge in California next month.
McIlroy said: "It was close the whole day. I had the better start, then Tiger started getting birdies on the back nine. I think it was pretty exciting for the fans and it would be great to compete more with Tiger like this – maybe down the home stretch in the majors.
"The growth of the game here has been huge even in the few years I've been visiting and I really hope that games like these can inspire some kids who want to play the game. I wouldn't be surprised if one of the next great players was to come from China. With it being an Olympic sport [from 2016], interest is growing."
Woods said: "We actually both played decent golf. We left a lot of putts out there and we could have really shot some low numbers. This is certainly not like most Mondays. To have this many people come out is pretty special; we're ranked No.1 and No.2 in the world, so a match like this can really promote the game in China. I've come here for 11 years now and it's amazing how much the game has grown."
On McIlroy, he added: "Over the past few years it has been great to see his growth. We'd be excited about a rivalry, but we'd want it to last for 10 to 15 years."