Dunga's men - minus suspended captain Neymar and defender David Luiz - looked set for a second defeat in six games when goals either side of half-time from Dario Lezcano and Edgar Benitez put Paraguay in a commanding lead.
Ricardo Oliveira's strike in the 80th minute gave Brazil hope, but they were reliant on Dani Alves' last-gasp strike to earn a point and break Paraguay's hearts.
The draw will paper over the cracks, though, as they were second best in Asuncion, and just two wins from their first six games means that the road to Russia is far from a smooth one.
The hosts could have been ahead before the 20-minute mark as Richard Ortiz got on the end of a dangerous free-kick but his flicked header was turned onto the post by Brazil goalkeeper Allison, who then produced a stunning save to deny Gustavo Gomez from close range.
Eventually the deserved breakthrough came five minutes before the half-time interval as Lezcano scored his third goal in two games.
Fresh from his brace in the 2-2 draw with Ecuador last week, the Ingolstadt striker rammed home from eight yards after a superb piece of play from Benitez down the left.
Benitez got himself on the scoresheet when Paraguay enjoyed the best possible start to the second half.
Roque Santa Cruz found Ortiz, who slipped Benitez in on goal with a fine pass and the winger made no mistake as his first touch created space and his second prodded the ball into the bottom corner in the 49th minute.
Missing the suspended Neymar, Brazil were bereft of any real attacking threat, though they thought they were back in it shortly after the hour when Gil climbed highest from a corner to head home but he was adjudged to have infringed his marker.
Brazil finally stirred and did make a game of it with 10 minutes remaining when Oliveira was on hand to stroke home a rebound after Justo Villar had spilled Hulk's shot from 20 yards.
Just when it looked like Paraguay were going to hold on for a famous win, Alves popped up with his first international goal in two years when he curled into the bottom corner to steal a point.