Joint overnight leader Dougherty fired a four-under-par 68 and Howell carded a blemish-free 67 in the rain to go to 12-under 132 at the $5 million event in Shanghai.
Woods stayed within striking distance at 10-under par despite an error-strewn 69 that left him tied for third with Australia’s Nick O’Hern, who shot a 67.
Woods made four birdies but struggled with his short game in the drizzly gloom at Sheshan International Golf Club.
The American fluffed a bunker shot on the seventh hole, slipped as he climbed out of the sand, then smashed his golf bag with his club in fury.
He bogeyed 16 after failing to clear a greenside bunker chipping from the rough and had to make a miraculous save at the par-five 18th after finding water with his second shot.
In contrast, Briton Kenneth Ferrie fired a hole-in-one and led for much of the second round until bogeys on 17 and 18 forced him to settle for a 69 and a five-way tie for fifth place.
Ferrie’s ace came at the sixth when he holed a four-iron from 193 yards.
Leading second round scores:
132 - David Howell 65-67, Nick Dougherty 64-68
134 - Nick O’Hern 67-67, Tiger Woods 65-69
135 - Kenneth Ferrie 66-69, Paul Casey 67-68, Thaworn Wiratchant 67-68, Zhang Lian-Wei 67-68, Robert-Jan Derksen 65-70
136 - Peter O’Malley 64-72, Ian Poulter 67-69, Thomas Bjorn 67-69, Vijay Singh 67-69, K J Choi 65-71, Michael Campbell 66-70
137 - Graeme McDowell 70-67, Jean-Francois Remesy 70-67
138 - Charl Schwartzel 68-70
139 - Peter Hanson 69-70, Arjun Atwal 69-70, Paul Lawrie 64-75, Lee Westwood 70-69
140 - John Bickerton 68-72, Gonzalo Fdez-Castano 70-70, Steven Bowditch 71-69, Simon Wakefield 68-72, Prayad Marksaeng 70-70, Thongchai Jaidee 67-73, Titch Moore 69-71.—AFP