Westwood, who needs to win in South Korea to be assured of retaining top spot, sank seven birdies but bogeyed three of the four par-three holes.
Australia's Brett Rumford leads the way after a nine-under-par 63 lifted him to 10 under for the tournament.
Ian Poulter eagled the 18th but finished two over to miss the cut.
The Englishman had started well with two birdies in his opening three holes but he bogeyed the 5th and 7th to fall back to two over par with the cut projected at one over.
He birdied the 12th, but bogeyed the 14th and dropped two more shots at the par-five 15th.
However, pars on the 16th and 17th left him needing an albatross on the par-five last to make the cut - his second shot missed the green and, although he finished with a deft chip-in to pick up two shots, the eagle was irrelevant.
Immediately after his round, Poulter tweeted: "Disgusted to miss the cut in Korea today, it's beyond pathetic, the harder I try at the minute the worse it is. This game keeps you guessing."
Westwood opened with four birdies on the front nine and carded three more as he attempted to climb up the leaderboard after a level-par first round.
Despite the three bogeys that checked his progress, the 38-year-old said: "Four under gives me a chance - six behind one and three behind second. I have a funny feeling a lot can happen on this golf course."
Westwood, who only returned to world number one after winning last week's Indonesian Masters, needs to finish at least fifth at Blackstone Golf Club in Icheon, to hold off current number two Martin Kaymer, who is not playing this week.
If Luke Donald triumphs at the PGA Tour Classic of New Orleans, where he is two shots off the lead after the first round, he will jump to number one, unless Westwood wins.
However, the day belonged to Rumford, who sank nine birdies in his bogey-free round.
"I didn't come to this week with that great form, but this is a funny game," he said. "The last two weeks I've not been playing well, I've been grinding everything out."
Denmark's Soren Kjeldsen and Spain's Miguel Angel Jimenez also went on birdie sprees, collecting seven apiece, and respectively carded 66 and 67 for a share of second on seven under.
Ireland's overnight leader Damien McGrane shot a level-par 72 and is tied for fourth with Rhys Davies of Wales (68) and England's James Morrison (69).
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