Fellow Brazilian striker Kleber also scored two for Cruzeiro in their 2-2 draw at Venezuela's Deportivo Italia in Group Seven but was sent off near the end for a bad tackle, his second yellow card offence.
In two Group Five matches played in Ecuador, modest Uruguayan side Cerro shocked Emelec 2-1 in the George Capwell stadium in Guayaquil while Ecuadorean champions Deportivo Quito were held 1-1 by Brazil's Internacional in the capital.
Washington, who also scored both goals in Sao Paulo's 2-0 home win over Mexican champions Monterrey a month ago, took his tally in South America's top club competition to four.
He felt his performance answered his critics after he was slammed for a glaring miss against Once Caldas two weeks ago just before the Colombian side scored their second goal for a 2-1 victory.
"Of course, against Once Caldas I had that chance, I didn't take it and the team lost," Washington was quoted as saying on Brazilian broadcaster Globo's sports website.
"But there are going to be lots of games when I'm not going to score and the team will lose. No one's unbeatable and no one's perfect. But also, many times, I'll settle (the game), like today," he said.
NEAR-EMPTY STADIUM
Washington opened the scoring with a left-foot shot against the run of play just before the hour and tapped in a cross in the final minute of the match, played in front of less than a thousand spectators at Asuncion's Defensores del Chaco stadium.
Once Caldas, champions in 2004, lead the group with seven points, one ahead of three-times winners Sao Paulo, after three matches. Monterrey have four points and Nacional none.
In Caracas, twice champions Cruzeiro struggled against Italia, who picked up their first point and scored their first goals after two defeats.
Kleber was sent off five minutes from time and Italia's substitute left back Rafael Lobo was shown a straight red card in the 89th, two minutes after coming on.
In Guayaquil, Cerro midfielder Pablo Caballero put his side in front early in the second half when he tapped in the rebound after Alvaro Melo's shot had hit the bar.
In the 66th minute, centre-back Claudio Dadomo took a free kick on the right just outside the box, blasting a rising shot between two defenders and past diving keeper Marcelo Elizaga into the top far corner to secure a second win for the Uruguayans.
Midfielder Pablo Perez pulled one back with a diving header 20 minutes from the end.
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