Twin strikes by Woods in the space of three minutes put New Zealand on winning course after the teams were level 2-2 at half-time.
Back to winning habit after being held to draws by Malaysia and Canada in their initial two outings, New Zealand took their points tally for five, while Pakistan have three points from two matches.
Pakistan had beaten Canada 3-1 in their opening fixture.
Pakistan opened the account in the eighth minute through Muhammad Arslan Qadir, who flicked in Ajaz Ahmed's cross just wide of goalkeeper Kyle Pontifex.
New Zealand drew parity in the 12th minute when George Muir's diagonal cross was deflected into the boards by Stephen Jenness.
Pakistan then forced seven penalty corners in the space
of three minutes, four of them in a succession before equalising in the 21st minute. Muhammad Irfan Jr found the target in a scrimmage following a penaty corner shot.
Pakistan tried to stage a comeback and exerted a lot of pressure on New Zealand, but could only reduce the margin by a goal. Qadir scored his second goal for Pakistan in the 52nd minute before New Zealand closed the gaps in their defence.
Earlier, fast-improving Canada posted their first victory in three outings by prevailing 3-1 over Japan.
After a goalless first half, Canada rode on two open field goals in successive minutes to take a 2-0 lead. Mark Pearson (34th minute) and Garbiel Ho-Garcia (35th) penetrated the Japanese circle to shoot on target before Japan pulled one back in the 42nd through captain Hiroki Sakamoto through a penalty corner.
The victory took Canada's points tally to four from three outings. They had picked up the first point from a 1-1 draw against New Zealand on Thursday.
Japan have suffered defeats in all their three outings.
