Canada came close to opening the scoring early on when Tesho Akindele found space inside the box, only to guide his right-footed effort straight at the keeper.
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The game moved from end to end in the opening gambit and Jamaica almost found themselves in front after 30 minutes when Simon Dawkins got an effort off towards goal, but he was thwarted by some last-ditch defending from David Edgar on the line.
Jamaica continued to impress after an imposed water break and they squandered another chance as Garath McCleary crossed for Giles Barnes, who headed high and wide of the target without testing the goalkeeper.
Canada shared much of the ball in the early stages of the second half, but yet again it was Jamaica who almost came up with the goods, this time as Barnes crashed the ball off the crossbar from a free kick.
Barnes and his teammates continued to push for an opener despite their missed chances and they nearly found the vital goal 20 minutes from time, although Barnes was to be outdone by some smart goalkeeping.
As the clocked ticked down, Jamaica's captain Austin ensured that they would not leave the Compass Stadium empty handed as he rushed into the box to head into the net from close range and seal an important last-ditch win.