Canada, which had largely been outplayed for most of the game but was seconds away from escaping with a point, couldn't clear a Martinique corner kick in the dying seconds of the match. The ball fell to Reuperne, who unleashed a screaming shot past Canadian goalkeeper Milan Borjan in the first game of the tournament for both countries.
The loss to a country of just 400,000 is the latest setback for a Canadian program that also failed to advance to final stage of World Cup qualifying for Brazil 2014.
After getting a few early chances on Sunday in front of the Martinique goal, Canada suddenly found itself on the back foot and looked completely out of sorts as the tiny island nation applied the pressure.
Marcus Haber had Canada's first chance in the 10th minute when he got his head onto a corner kick from Will Johnson. Haber made good contact but Martinique goalkeeper Kevin Olimpa dropped to his left and made the save.
Johnson fed in another corner in the 13th minute that was met by defender Doneil Henry, but his header went wide.
After that, Martinique took the play to the Canadians. Frederic Piquionne got past Canadian midfielder Samuel Piette and found Kevin Parsemain on the left side in the 20th minute, but Borjan came off his line to make the save.
Apart from that save, Borjan had a shaky first half. He chose to punch catchable crosses on two separate occasions and both times Martinique was gifted quality chances.
Though it was a tough first half, Borjan saved Canada twice in the first five minutes of the second with quality saves to keep the game scoreless.
After surviving the Martinique onslaught, Canada finally got on the front foot with about 25 minutes remaining.
In the 64th minute, Russell Teibert controlled a cross from the left side and hit a shot that was tipped over for a corner.
Not long after, Edgar had a high, looping header go off the top of the crossbar and out for a goal kick.
The tournament gets much harder for Canada from here. Next up in Group A is a tough match against Mexico on Thursday, while Martinique takes on Panama.