Some distance into the second half, the Spaniards led by a full six goals, but despite several Brazilian expulsions at the end, the South Americans both caught up and passed.
When Rogério Moraes put 29-28 with 21 seconds left to play, the premiere beats in Group B were close.
But the reigning European champion ultimately prevented a difficult loss.
With only seven seconds left, Raul Entrerrios was able to save the point for Spain.
In Group C, last year's European Championship finalist Croatia also had major concerns with Japan, which finished in last place in the last World Cup.
The Japanese led for a while with six goals, pushed the gold candidate all the way in and, like Brazil, were close to an unexpected victory.
But Croatia also got a point after Ivan Cupic equalized to 29-29 on penalties with nine seconds left.
Friday's overrun was Germany in group A. The Germans won over Uruguay by a full 43-14 and the fact that the Uruguayan goalkeeper Felipe Alfonso González was named the match's liar probably says something about the class difference between the teams.