Woods started the day at 1-over, eights shots back of Stephen Leaney and James McLean, and fell ten off the pace after a double bogey at the par-4 first Saturday.
Incidentally, Woods is a combined 8-over-par on his first holes of each round, including last week's Mercedes Championships.
Under heavy rain, Tiger hit his drive in the long, wet rough on the opening hole, and was only able to advance his second shot some three feet.
The worlds No. 1 recouped with birdies at the second and fourth holes, and then drove the 310-yard, par-4 sixth. Woods, who averaged nearly 33 putts over his first two rounds, knocked in the seven-foot eagle putt to get back into red numbers for the tournament.
For the first time all week, Woods failed to post a birdie on a par-5, when he parred the seventh hole; however, he rolled in an 18-foot birdie putt at the par-4 eighth to climb to minus 2.
Despite the double at the first, Tiger made the turn in 3-under 32. He then parred Nos. 10 and 11, and was in the fairway at the 12th when play was halted.
Woods, recipient of a $2 million appearance fee, opened in 1-under 70, but struggled mightily in a windy second round, birdieing the par-5 finishing hole for a round of 73.
Only nine players, including 13-year-old qualifier Jae An (71), have finished their third rounds. Fourteen players in the 67-man field have yet to complete a single hole.
Nick O'Hern did make it out on the Paraparaumu Beach course, though he certainly wishes otherwise. O'Hern, four off the lead at 3-under, lost his tee shot at the first and took five shots to reach the green before the horn blew to suspend play.
Full-field scores from the New Zealand Open