Shota Horie and Kosuke Endo scored tries and James Arlidge added 13 points from the boot for Japan, who were seeking to end their Pool A campaign on a high.
But Canada, who beat Tonga earlier in the tournament and meet New Zealand in Wellington on Sunday, scored tries through DTH van der Merwe, Phil Mackenzie and Ander Monro. James Pritchard kicked a conversion and Monro a penalty before the latter added another penalty late on to tie the scores and prevent Japan ending a winless World Cup run stretching back to 1991.
It was a repeat of the result between the sides four years ago, when they drew 12-12 in France.
Van der Merwe broke through Endo's tackle to score in the eighth minute after Canada camped on Japan's line early on. Pritchard converted.
Japan responded immediately, with Horie barging over from close range and Arlidge added the extras.
Japan went in front with an Arlidge penalty before they were rewarded for a spell of sustained pressure on the stroke of half-time when Arlidge released Endo to score under the posts.
Canada responded four minutes into the second half, with Mackenzie racing round from his left wing to touch down in the right corner.
A period of sustained pressure saw Canada emerge with a Monro penalty, but they then conceded a penalty due to poor discipline and Arlidge restored the five-point lead.
Canada conceded another penalty eight minutes from time and Arlidge put his side eight points clear.
Further sustained pressure from Canada was rewarded when Monro barged over, but he could not add the conversion.
He made amends, though, kicking a penalty two minutes from time to tie the scores, before Arlidge screwed a drop-goal attempt wide as Japan were forced to settle for a draw.
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