Paulinho and Gabriel Jesus struck in the space of three second-half minutes at the Allianz Parque in Sao Paulo before the latter sealed the deserved victory late.
Tite's side dominated the first half without capitalising, before a Claudio Bravo error allowed Paulinho to open the scoring.
Jesus then struck twice, completing a sensational qualifying campaign for CONMEBOL group winners Brazil.
It meant South American champions Chile needed other results to go their way to move into a play-off with New Zealand, but Peru's equaliser at home to Colombia saw Juan Antonio Pizzi's men finish sixth.
Ederson replaced Alisson in goal, while Marquinhos took Thiago Silva's place in the centre of defence.
For Chile, there were three changes to the side that claimed a dramatic 2-1 win at home to Ecuador.
The big blow was Arturo Vidal's suspension, with Jose Fuenzalida, Charles Aranguiz and Jean Beausejour coming in for the midfielder, Eugenio Mena and Francisco Silva.
Both teams made a bright start in Sao Paulo, but the biggest early cheer was for Argentina falling behind in Ecuador, although Lionel Messi would inspire a comeback in Quito.
Brazil looked the more dangerous of the two teams in the opening stages, and Neymar had a penalty shout turned down.
However, the Paris Saint-Germain star should have put the hosts ahead in the 16th minute, only to be denied by a good Bravo save.
The hosts were the better of the two sides in the opening 45 minutes, and they wasted another great chance six minutes before the break.
Renato Augusto found space down the left and crossed for Jesus, who headed straight at Bravo from close range.
The hosts finally took a deserved lead with two goals in three minutes.
A long-range Dani Alves free-kick was spilled by Bravo into the path of Paulinho, who tapped in the 55th-minute opener.
Just two minutes later and it was 2-0, Neymar unselfishly squaring for Jesus to tap in after being released in behind.
Brazil looked the more likely to score again as Chile pushed, and they sealed their win in additional time.
With Bravo stranded after going up for a corner, Jesus tapped in the easiest of goals from a Willian pass in the 93rd minute.