The Group Six match at the Centenario in Montevideo was marred, however, by fighting between Nacional fans and police that left 13 officers hurt and 38 people arrested, according to a Uruguayan Interior ministry statement.
The violence, a regular blight of the competition, began when a group of home spectators objected to being ordered to stay in the stadium until the visiting supporters had left, a method often used in South America to avoid clashes between rivals fans.
Former France striker Trezeguet, who grew in Argentina and dreamed of playing in South America's top club competition on his return to the country in 2012, came on a substitute and broke a 2-2 deadlock with two goals in the last 15 minutes.
Trezeguet put Newell's ahead in the 75th minute, tapping home with the Uruguayan three-times champions down to 10 men from the 73rd when Rafael Garcia was sent off for elbowing Gabriel Heinze.
The 36-year-old sealed the win in the 90th minute with a low shot that beat Andres Scotti, standing in as goalkeeper after Nacional also had Jorge Bava sent off in the 81st for handball outside his box with all their substitutions completed.
"To achieve important things you have to win at home and away. This (win) has got us out of that negative away run," Newell's coach Alfredo Berti said. His side had gone 10 away games in all competitions without a win.
Newell's are looking to lift the trophy for the first time after twice finishing runners-up, the first time to Nacional in 1988.
The Argentine side went top of the group with Brazil's Gremio, who have a game in hand, on eight points apiece with Colombia's Atletico Nacional hot on their heels on seven.
The result eliminated Nacional, who have taken one point in five matches, and came at the same time as fellow Uruguayans and five-times champions Penarol were also knocked out thanks to another Argentine victory.
Arsenal's 3-1 away win over Deportivo Anzoategui of Venezuela made sure they finished second in Group Eight with one match to spare to reach the knockout phase for the first time.
Mexico's Santos Laguna won the group after their 4-1 rout of Penarol on Tuesday. With one match to go, Santos have 13 points, Arsenal nine, Penarol four and Anzoategui two.
They were joined in the round of 16 by 1994 champions Velez Sarsfield, who won 3-1 away to Atletico Paranaense of Brazil on a near perfect night for Argentine teams.
Velez took an early lead through midfielder Agustin Allione but were pegged back by Drausio's equaliser in the 54th, three minutes after the Brazilian side had their Spanish reserve Fran Merida sent off for repeated dissent from the bench.
Striker Lucas Pratto put Velez ahead on the hour and substitute Hector Canteros made sure in added time, three minutes after team mate Emiliano Para was red carded.
- Sports & Recreation