The once prolific duo at Real Madrid helped Brazil to a 1-0 win over Paraguay in Sao Paulo on Tuesday (Wednesday AEST).
Brazil's win means Ecuador also progress after a 0-0 away draw against Peru in Lima.
Defending champions Argentina, held to a 1-1 draw by Colombia, had already qualified for next year's global tournament in the US, Canada and Mexico.
Ecuador and Brazil each have 25 points in the standings, but the Ecuadorians are in second spot based on victories. The two nations are 10 points behind Argentina but, crucially, more than six points clear of the seventh-placed team with two games remaining in the qualifying campaign.
The top six teams in South America earn direct entries to the 48-team World Cup.
In Sao Paolo, a mistake by Paraguay's defence, a low cross by Cunha and a gentle touch by Brazil's new No.10 produced the only goal of the match.
"We needed to win here for our people. Now we have more time to work, see what we can improve," Vinicius said after the match.
He won't play Brazil's next game in qualifying against Chile because of suspension.
Chile will miss a third consecutive World Cup after losing 2-0 at Bolivia to remain last in the 10-nation round-robin competition, a result that cost head coach Ricardo Gareca his job.
Uruguay beat Venezuela at home 2-0, edging closer to one of the six direct World Cup spots with 24 points.
Venezuela, with 18, are one ahead of Bolivia in the contest for seventh place that grants an intercontinental playoff berth.
In Buenos Aires, Luis Diaz opened the scoring for the visiting Colombians in the 24th minute, before Julian Alvarez equalised for the home side in the 81st minute.
Colombia, with 22 points, will play for their World Cup future later this year against Bolivia and Venezuela.
In Europe, Memphis Depay tied the scoring record for the Netherlands men's national team with two goals in the side's 8-0 World Cup qualifying win over Malta.
Depay scored in the ninth and 16th minutes for his 49th and 50th goals for the Netherlands at Euroborg Stadium in Groningen on Tuesday.
In doing so he equalled the Dutch record set by team great Robin van Persie.
Depay hit 50 goals in his 102nd game for the Netherlands, while van Persie's 50th came in his 101st game in 2015.
Finland's game against Poland in Helsinki was suspended because of a medical emergency in the stadium with Finland leading 2-1. The game later resumed and the home side hung on for the win.
Finland lead Group G by a point from the Netherlands, but have played two more games. Poland dropped from first to third.
In other qualifiers in Europe, Austria beat San Marino 4-0, Romania won 2-0 against Cyprus, Serbia beat Andorra 3-0, and Latvia and Albania fought out a 1-1 draw.
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