Mexico were frustrated for long spells against Trinidad and Tobago but eventually prevailed with a Raul Jimenez strike late on.
Panama had a far easier time of it, beating Cuba 6-1 to cruise into the last four of the competition.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.