The reigning Copa America champions came into the match against their arch rivals knowing that a win might not be enough to secure their ticket, but a draw could be.
And Chile's 2-0 defeat at home to Ecuador, coupled with Uruguay's 3-0 loss to Bolivia, sent Argentina through.
It caps a fine year for Argentina and Lionel Messi, who won their 15th Copa America in July with a 1-0 final victory over Brazil at Rio de Janeiro's iconic Maracana stadium.
"If we analyze this year, it was beautiful. What we've been through with the fans ... everything was complete," said Rodrigo De Paul.
Argentina welcomed back six-time Ballon d'Or winner Messi to their starting line-up while star forward Neymar missed out for Brazil.
But Messi was unable to inspire his team in a match of few chances, against opponents who booked their ticket to Qatar on Thursday with a 1-0 win over Colombia.
Brazil remain top of the qualifying group, six points clear of Argentina, who took their unbeaten run to 27 matches.
"We played very well in every match this year. We're already qualified for the World Cup," said Brazil's Fred.
"Today we failed in the final third but the most important thing is coming away without a goal against."
Brazil wasted a two-on-two break when Fred's pass forced Vinicius Junior wide, and his first touch ran out of play.
It summed up a match that never caught fire and in which almost nothing came off from either side.
Quick-thinking Matheus Cunha tried to score the goal of the qualification campaign when attempting to chip Argentina goalkeeper Emiliano Martinez from inside his own half, but his effort sailed over the crossbar.
Argentina came alive in the last five minutes of the half as De Paul managed the hosts' first shot on target, although Alisson Becker dealt with it comfortably in the Brazil goal.
Brazil had only managed one shot on target themselves in the first 45 minutes, and that was a weak effort by Fred.
The major talking point was how Argentina center-back Nicolas Otamendi escaped a red card for elbowing Raphinha in the face, drawing blood.
According to reports, Raphinha needed five stitches at half-time.
Much-maligned Manchester United midfielder Fred almost became the unlikely hero in the second period when he came closest yet to breaking the deadlock, clipping the top of the bar with Martinez beaten.
But there was little else to get excited about, with neither goalkeeper seriously tested.
Even a late effort from Messi after jinking past Fred was straight at Alisson.
- Bolivia, Peru close in -
Twice world champions Uruguay's hopes suffered a huge blow as they were thrashed at 10-man Bolivia, leaving them seventh in the 10-team group, although only a point off the last automatic qualification place.
A brace from Juan Carlos Arce and another from Marcelo Martins gave Bolivia a comfortable victory that keeps their qualification hopes alive.
Even the dismissal of Carmelo Algaranaz 15 minutes from the end, with the score 2-0, did not ruin Bolivia's night.
A third win in four matches left Bolivia just two points behind Colombia in fourth.
Colombia are hanging on by their fingernails to the final qualification berth after a fifth straight game without a goal -- four of which ended 0-0.
Colombia could not force a winner at home to Paraguay, even though the visitors had Adrian Cubas sent off six minutes from time.
Peru's second win in a row, 2-1 away to rock-bottom Venezuela, put them level on points with Colombia in the intercontinental play-off spot.
Gianluca Lapadula and Christian Cueva goals either side of a Darwin Machis strike for Venezuela gave Peru a crucial win.
Goals from Pervis Estupinan and Moises Caicedo condemned Chile to defeat, and dropped them from fourth to sixth.
They also had Arturo Vidal sent-off in the first half for a high boot.
Ecuador sit third, six points ahead of Peru in fifth with just four matches left.
(For more sports news and updates, follow Ahram Online Sports on Twitter at @AO_Sports and on Facebook at AhramOnlineSports.)