A second half strike from Santos player Lucas Lima salvaged a vital point for Brazil after Argentina had taken the lead midway through the half thanks to an Ezequiel Lavezzi strike.
Lavezzi's Paris Saint-Germain team-mate David Luiz was sent off for a second yellow card in the dying minutes but Brazil hung on for the draw.
The result leaves Argentina winless after three games of South America's marathon qualifying campaign, with only two points from a possible nine.
Friday's match at the Monumental Stadium in Buenos Aires had been delayed by 24 hours after a deluge made the pitch unplayable on Thursday.
Argentina, missing a glut of injured stars including Lionel Messi and Sergio Aguero, started the stronger against a Brazil side who welcomed back suspended striker Neymar.
Neymar however was largely anonymous for long periods as Argentina got on top early on and opened up Brazil with ease on several occasions.
The only surprise was that it took Argentina more than half an hour to get on the scoresheet. The goal came after superb interplay between Argentina's powerful attacking front three.
Angel Di Maria darted inside on a jinking run near halfway before releasing Gonzalo Higuain down the right flank.
The Napoli striker looked up and picked out Lavezzi with a superb low cross for the France-based star to ram past Alisson Becker for 1-0 on 34 minutes.
It was no less than Argentina's bold attacking approach deserved.
Argentina might have taken an early lead after only two minutes, when Facundo Roncaglia drew a save from Allison from a wide angle with looping shot.
Moments later Di Maria embarrassed Luiz down the right flank, turning the midfielder inside out before firing in a low cross which flew across the face of goal. Brazil escaped however, with no Argentinian attacker on hand to meet Di Maria's centre.
Luiz might have levelled for Brazil shortly before half-time but could only head over the bar from close range after Willian's freekick from the right.
Argentina started the second half in the same vein, with Ever Banega only being denied a goal from a tight angle when his fierce low shot struck the foot of the post in the 46th minute.
But it was Brazil who struck next, getting on level terms through a cleverly worked goal on 58 minutes.
Dani Alves curled a sublime cross to the far post with the outside of right boot to pick out Douglas Costa, who headed firmly against the bar before Lima smashed in the rebound on the volley.
Buoyed by the goal Brazil looked the likelier to grab a winner, with Willian going close with a shot deflected over the bar.
Manchester City defender Nicolas Otamendi went close with a late header which flew just wide.
In the closing minutes Luiz was shown a red card for two bookings within as many minutes, but Brazil held on for the draw.
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