The Mexico goalkeeper produced a flurry of show-stopping saves over the course of the match to hold Brazil scoreless in a World Cup game for just the third time since the 1998 final.
The draw sees the two nations improve to four points apiece, ensuring that they head into the final matchday at the Group A summit.
"A 0-0 is never a good result but it reflects how evenly contested this game was," Brazil coach Luiz Felipe Scolari said after the match. "This (team) continues to evolve, keeping the same system for the last 20 games. The team's doing well. People have to be aware that we're coming up against good-quality teams. Being on top of the group doesn't make this a good result, because we'd have qualified with a win, but we have to show respect for our opponents, who are a very good side."
The best chance of the opening period fell to Brazil in the 26th minute when Dani Alves delivered a superb cross to the back post that was met by Neymar's header, but the Barcelona man was denied by Ochoa's sprawling stop, perhaps the best save of the tournament thus far.
The Mexicans dictated play for much of the second half, growing in confidence as the match wore on, but Brazil was able to keep them in check by holding them to long-range efforts.
Brazil took back some momentum inside the final half-hour and nearly went in front in the 69th minute when Neymar settled a cross from Bernard and lashed a shot on frame, but Ochoa was equal to the task once again, parrying the attempt to safety.
Ochoa's heroics continued in the 86th minute when Neymar's cross was met by Thiago Silva, but the defender put his powerful header directly at the Mexico 'keeper, who was able to punch the ball away.
Mexico applied some late pressure with Andres Guardado collecting a short corner kick in the 90th minute and almost picking out the upper corner with a left-footed effort, but he ultimately saw his shot sail just over the crossbar.
The Mexicans were able to create another solid scoring opportunity just one minute later as Raul Jimenez uncorked a shot from the right side of the box. Julio Cesar was quick to react and did well to stop the shot, but he parried the ball directly into the danger area in the center of the box. Mexico, though, was unable to pounce on the rebound, preventing the CONCACAF nation from stealing all three points.
"We (the coaching staff) had a plan, but the credit must go to the players, who played a great game," Mexico coach Miguel Herrera said. "We picked up a point but we've not achieved anything solid just yet. We're in the group and battling it out for a place (in the next round), even with Brazil. We've still got another group game to play and, like always, we'll be going all out for the win."
Brazil and Mexico will close out the group stage on Monday with the five-time champions facing Cameroon and Herrera's men taking on Croatia.