The decisive moment came with the 28th penalty attempt, when Adam Froeze beat Manchester to initiate jubilant scenes among the Canadians.
Of the New Zealand penalty takers, veteran Ryan Archibald missed all three attempts - with one the ball crossed the goal line fractionally after the hooter sounded to signal his eight seconds to score were up.
Captain Simon Child missed with both his chances. Blair Hilton's second attempt, which would have won the game, was deflected onto the crossbar.
Midfielder Steve Edwards was easily the pick of the New Zealanders, nailing all three attempts with aplomb.
In normal time, New Zealand were unable to score with four penalty corner attempts.
They now face Australia in the Oceania series, the winner guaranteed a trip to Rio. After that, New Zealand must look at another avenue to try and qualify for Rio.
Meanwhile the women's Black Sticks were beaten 3-1 by the Netherlands in the first of two warmup tests for their world league semifinal starting next week.
Brooke Neal scored New Zealand's goal from a penalty corner in the final quarter.
The teams meet a second time tomorrow night at the Noordwijkse club before heading to Antwerp, Belgium for the tournament, which begins on June 20.