The 37-year-old Englishman, who ended Woods's 281-week reign at the summit last weekend, played through the niggling pain of ankle and calf injuries to sit just one shot behind Italian Francesco Molinari at the top of the leaderboard.
Westwood, Woods, who started with a 68, Martin Kaymer and Phil Mickelson occupy the top four places in the rankings and a win for any one of them this week would guarantee the No 1 spot.
"I think the world rankings are reflective of how competitive world golf is at the moment. Nobody is out-and-out world No 1," said Westwood after playing his first competitive round since last month's Dunhill Links Championship. "I think that's partly to do with Tiger not having played quite so well this year and partly to do with Tiger having made everybody else elevate their game," he added.
"Tiger's a victim almost of his own brilliance. We have all had to work harder and we have closed the gap, I guess."
Westwood said he was still not 100 per cent fit and applies iced cold packs to his ankle every night to boost the healing process.
"As the round goes on, it starts to ache and I lose control and power a bit," he said. "I have to continually remind myself when I'm swinging out there to sort of reinforce it.
"I like to go out there and just sort of free wheel and play with a clear mind and I have to sort of consciously think about it all the time."
Westwood, who offset a lone bogey with seven birdies, said he did not feel under any extra pressure to defend his new position as the man to beat.
"I don't think I need to reinforce why I'm world No 1. I didn't really go out there (today] with any particular thought to perform like the world No 1," he added.
"I think you get there as a result of good performances but it's nice to show everybody there is a particular reason why I got to this stage. I think I did that today."
One shot behind Westwood are Sweden's Henrik Stenson, Japan's Yuta Ikeda and South Korean Noh Seung-yul.
Woods shot a solid 68 to sit three shots behind Molinari in a tie for sixth, a stroke ahead of Scotland's Richie Ramsay and defending champion Mickelson and four clear of Germany's Kaymer.
Woods overcame a first-hole bogey to roar back into contention with five birdies. "It felt good today. The things that I've been working on felt good. I hit a lot of good golf shots," he said.
"I got to No 1 in the world by winning golf tournaments and I've had that sustainability for a number of years by doing that. The whole idea is to win golf tournaments and this is no different.The reason why we tee it up is to win."
Molinari, a member of Europe's victorious Ryder Cup team at Celtic Manor, carded seven birdies in his bogey-free effort at Sheshen International GC to head the leaderboard.
Starting at the tenth, the 27-year-old made steady progress over his opening nine holes with three birdies to reach the turn in 33 but by the time he had confidently stroked in a putt at the sixth for a fourth consecutive birdie on the back nine, he had overhauled morning frontrunner Ikeda for the lead. A long birdie putt on the seventh just slipped past the hole but he then needed a beautifully-judged chip from the fringe on the ninth to save par and secure the first-round lead.
Alongside Woods are Luke Donald and Pablo Martin. Donald did not drop a shot as he sank four birdies while Martin picked up five birdies and one bogey.
The group of nine players on 69 also features Ross Fisher and Open champion Louis Oosthuizen, who revealed that he has to wear a specially-fitted brace on his injured ankle for the next three months.
Oosthuizen tore ligaments on a hunting trip in late September when he returned home to attend the wedding of fellow South African Charl Schwartzel. The 28-year-old had shot a deer and was running after the wounded animal when he tripped and fell in a pot hole.
This is his first event since finishing tied fourth in the KLM Open and the injury forced him to miss an emotional return to St Andrews for the Dunhill Links Championship.
"It was nice to come back after a long lay-off and shoot a 69 as I am very restricted on my shots and that's just one shape, a very big draw," he said. "But the good thing is that my short game is still there.
"I am wearing this brace that I have to wear for the next three months and till at least the end of January.
"I've had a lot of treatment on the ankle and I am at the stage where I am really not going to hurt it anymore but then I do feel it hurting on some shots.
"But I want to play as many events as I can to get my confidence back up."