The five-times champions beat Paraguay 3-0 on Tuesday for their eighth successive win in the South American qualifying competition.
That in itself was not enough to confirm their participation in Russia but Peru's surprise 2-1 win over Uruguay in a later game guaranteed Brazil a top-four finish.
With four rounds of fixtures remaining, Brazil have 33 points, followed by Colombia (24), Uruguay and Chile (23). Argentina (22) are currently in fifth place, which earns a two-legged playoff against the top-ranked Oceania region side.
Uruguay and Argentina still have to face each other which means it is impossible for both to overtake Brazil.
Argentina dropped down the standings after losing 2-0 away to Bolivia at high altitude in La Paz, weakened by the absence of Messi as he began a four-match suspension.
The five-times world player of the year was banned less than six hours before kickoff for swearing at a linesman in the previous match, a 1-0 win over Chile.
He will now only be available for the last of Argentina's games, a potentially key match in Ecuador.
Russia are guaranteed a place as hosts.
(Writing by Brian Homewood in Berne; Editing by John O'Brien)
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