The Argentine side began the match in second place in Group Seven knowing only a heavy defeat and a good win for Universidad de Chile at Venezuela's Deportivo Lara could endanger their chances of going through.
The Chileans beat Lara 3-2 and Newell's, who missed some good chances on the counter-attack, had to cling on for a place in the knockout phase despite their goal difference over "La U" being dramatically reduced.
Newell's woes began after half an hour when goalkeeper Nahuel Guzman brought down Olimpia midfielder Sebastian Ariosa and was sent off, Uruguayan Juan Manuel Salguiero putting three-times champions Olimpia ahead from the penalty spot.
Salgueiro and former Newell's striker Juan Carlos Ferreyra finished with two goals apiece after the Argentine side had hit back with a fine equaliser from Milton Casco early in the second half.
Former champions Palmeiras, relegated to the Brazilian second division, qualified for the knockout phase with a 1-0 home win over Paraguay's Libertad in Group Two.
Striker Charles scored the winner early in the second half and Palmeiras defended their lead with ten men for the last half hour after Wesley was sent off.
Libertad face Argentina's Tigre next Thursday at home in Asuncion for the other qualifying berth in the group with a draw enough to see the Paraguayans through.
Other qualifiers include Brazilian holders Corinthians, six-times champions Boca Juniors and Velez Sarsfield of Argentina, three-times winners Nacional of Uruguay and Ronaldinho's Atletico Mineiro, favourites to lift the trophy for the first time.