After a goalless first half, Neymar soon gave Brazil the lead before substitute Firmino put the game out of Mexico's reach during the closing stages.
Tite's team progress through to the quarter-finals having registered their third consecutive clean sheet and Selecao will now face the winners of the clash between Belgium and Japan.
Just five minutes had passed before Neymar got his first shot away - a 30-yard strike which was palmed away by Guillermo Ochoa - but it was Mexico who had the better of the opening stages and troubled Brazil's backline with their movement and intensity.
However, their spell of pressure passed without Alisson being tested and Brazil soon began to dominate possession as Mexico reverted back to defending deep in the hope for opportunities to launch a counter-attack.
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 Manchester City forward then saw another effort saved after moving past two Mexico defenders and before the first half had come to a close, Neymar had drilled a 30-yard free kick marginally off target.
After the restart, both teams showed their intent to break the deadlock with Philippe Coutinho being superbly denied by Ochoa from 12 yards and Mexico's Jesus Gallardo advancing from the halfway line before curling over the crossbar from distance.
Moments later, however, Brazil went in front. Neymar started the move by playing in Willian, who advanced into the penalty area before delivering a low cross to the back post where Neymar was able to slide in and convert from three yards.
Brazil quickly looked for a second but Ochoa was keeping Mexico in the game, firstly keeping out a first-time strike from Paulinho from 12 yards before tipping a fizzing effort from Willian over the crossbar.
Their frustration continued into the closing stages and Brazil made sure of victory with two minutes of normal time remaining as Firmino tapped home from close range after Neymar's toe-poke had been saved by Ochoa.
BRAZIL (4-3-3): Alisson; Fagner, Silva, Miranda, Luis; Paulinho (Fernandinho 80'), Casemiro, Coutinho (Firmino 86'); Willian (Marquinhos 91'), Jesus, Neymar
MEXICO (4-2-3-1): Ochoa; Alvarez (Dos Santos 55'), Salcedo, Ayala, Gallardo; Marquez (Layun 46'), Herrera; Lozano, Vela, Guardado; Hernandez (Jimenez 60')