Mexico, rank outsiders who have not qualified for Olympic volleyball since hosting the Games in 1968, capitalised on numerous errors from Brazil to win the first set 25-23.
But a raucous home crowd, who jumped to their feet for every winning point, and an improved serve, allowed Brazil to fight their way back to win 23-25, 25-19, 25-14, 25-18.
After launching a signed ball into the cheering crowd, captain Sergio Santos admitted nerves might have got to the team.
"Those who have never competed in an Olympics before felt a difference playing with those rings on the floor," Santos, who is playing his fourth Olympics, told reporters.
"We have it in our heads that we always need to win, that's the pressure that surrounds the Brazilian team... But we know we'll only win this title by playing well," he said.
Brazil play Canada on Tuesday in their next match in Pool A.
Earlier in the day, Italy breezed past France in straight sets, laying down a marker that they are also ready go far in the competition. They won 25-20, 25-20, 25-15.
(Reporting by Stephen Eisenhammer)
