Barcelona superstar Neymar scored a dazzling solo goal after Liverpool forward Philippe Coutinho had opened the scoring for Brazil as the five-time world champions notched an eighth straight qualifying victory.
The win at Sao Paulo's Arena Corinthians means Brazil are all but guaranteed to extend their record of never failing to qualify for the World Cup by securing their place in Russia.
Tuesday's victory sees them lead the 10-team standings by nine points with four games remaining.
After demolishing the Uruguayans 4-1 last Thursday in Montevideo, Brazil were made to wait for the breakthrough against Paraguay.
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The goal they craved finally came on 34 minutes, with Coutinho playing a one-two with Paulinho before burying a low finish into the bottom corner.
Neymar had a chance to make it 2-0 in the 53rd minute from the penalty spot only to see his kick saved by Anthony Silva.
Neymar's dribble ended with him curling in a shot which took a slight deflection on its way into the Paraguayan goal. Real Madrid defender Marcelo added a late third to seal Brazil's win.
- No Messi, big problem -
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But while Brazil celebrated, Argentina and Messi were left digesting another stumble in their progress towards Russia as they slumped to a 2-0 defeat in La Paz.
Argentina had been rocked just hours before kick-off after confirmation Messi had been hit with a four-match ban following a ruling from disciplinary chiefs at world governing body FIFA in Zurich.
Messi's suspension left Argentina coach Edgardo Bauza forced to make a hasty reshuffle to his starting line-up, bringing in Atletico Madrid's Angel Correa in attack while leaving Manchester City's Sergio Aguero on the bench.
But Argentina, clearly struggling in the thin air of La Paz, which is 3,600 metres (11,800 feet) above sea level, were well beaten at the Estadio Hernando Siles.
Bolivia, desperate for three points, tore into Argentina from the opening whistle, spending long periods camped around their opponents area.
The defeat leaves Argentina languishing just outside the automatic qualifying places following results elsewhere Tuesday.
Chile moved up to fourth place with a 3-1 win over Venezuela in Santiago, Arsenal star Alexis Sanchez opening the scoring with a stunning early free-kick. Esteban Paredes scored twice for Chile to give the host a 3-1 lead before Salomon Rondon pulled a goal back for Venezuela.
In Quito, Real Madrid star James Rodriguez scored one goal and set up another for Juan Cuadrado as Colombia beat Ecuador 2-0.