After two 0-0 draws, it took spot kicks to separate the sides, with Newell’s eventually winning 10-9.
Olimpia are also into the last four after controversially beating Brazilian champions Fluminense.
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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.