Brazil would have booked a round of 16 berth had they beaten Mexico but Ochoa produced at least two stunning saves in a heroic display to deny the Selecao a win in a high-voltage Group A clash here.
The 28-year-old Ochoa, who plays in France for AC Ajaccio, first thwarted Neymar's 26th minute header with a spectacular dive to his right and then blocked Thiago Silva's headed attempt in the 87th minute to the huge groan of the sea of yellow-clad local fans.
The big match of the day was, however, the contest between South American rivals Brazil and Mexico.
Superstar Neymar, who scored twice in Brazil's 3-1 opening match win against Croatia, had plenty of ball possession and made some threatening runs into the rival box under hot and humid conditions at Estadio Castelao.
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But ultimately, the five-time champions failed to break down the stubborn Mexican defence and the seemingly impenetrable wall thrown around their goal by Ochoa. Mexico survived the grinding offence from Brazil and frustrated the hosts' march to the second round.
In a Group H match in Belo Horizonte, Belgium made a stunning rally to beat Algeria 2-1 with two second half goals.
Widely billed the dark horses to lift the trophy, Belgium had to toil hard to erase the 0-1 deficit after Algeria had taken a surprise lead in the 25th minute against the run of play through a penalty kick conversion by Sofiane Feghouli.
Belgium, whose most of players ply trade in top European clubs, turned the match on its head with two goals in the space of 10 minutes.