With Germany already out of the running, the Brazilians have a good opportunity to leave Die Manschafft further in the rearview mirror as they head into a quarterfinal clash against the victor of Belgium and Japan.
Neymar then began Brazil's awakening by brilliantly turning Edson Alvarez on the left side of the area, only to be denied by Ochoa. After being disqualified from qualifying in 1990, Mexico have suffered seven successive defeats in the round of 16 stage since 1994.
Brazil progress through to the World Cup quarter-finals as Neymar and Roberto Firmono net in the second half to secure a 2-0 win over Mexico in Samara.
Veteran defender Marquez was used off the bench earlier in the tournament in Russian Federation but started for Mexico today after appearances in 2002, 2006, 2010 and 2014.
Neymar went close in the 25th minute as the attacker drifted past Edson Alvarez before seeing a shot blocked by Ochoa, while Gabriel Jesus was not too far away with a left-footed volley from inside of the area.
The goal also made Brazil the most prolific team in the history of the World Cup with 227 goals, surpassing Germany - who were knocked out in the first round for the first time since 1938 - with 226.
Brazil became the all-time leading goal scorers at the World Cup in Monday's 2-0 win over Mexico.
Paulinho nearly doubled the lead before the hour, but his shot inside the box was kept out by the excellent Ochoa, who then had to tip Willian's fizzing drive over the bar.
Neymar, whose foul exaggerations were a point of pre-match talk from Mexico captain Andres Guardado, then drew the ire of the El Tri fans in the crowd of 41,970 by rolling theatrically on the ground after Miguel Layun stepped on his ankle in the 73rd minute.
Neymar scored a 51st minute goal to put Brazil up 1-0 against Mexico.