The Canadians, ranked 14th, six places lower than the Black Sticks, had the better of the first quarter. New Zealand looked sluggish and by halftime Canada had enjoyed 65 percent of possession and had got in double New Zealand's three shots.
New Zealand improved in the third quarter, Nick Wilson and Shay Neal prominent in their attacks and in the 15-minute block, they won six of their penalty corners, the last of which was whipped past impressive Canadian goalkeeper Anthony Kindler's left into the goal.
Woods and Neal both had chances in the closing stages as Canada clearly sat back hanging on for the point.
New Zealand finished up with 27 circle penetrations to Canada's 12, and 14 shots to six by Canada.
"We had a poor performance in the first half and let Canada dominate us," coach Colin Batch said.
"We looked tired and I think there was some residual effects from our first game but we need to get better at handling that."
Batch liked the second half improvement, and the number of chances created. Not grabbing them, however, has left him frustrated.
After a rest day, New Zealand next face 10th ranked Pakistan on Saturday night, knowing it's time for the defending champions to start winning, but equally knowing they are still very much in the tournament.
World No 1 Australia kicked off their campaign with a 5-1 win over India.