Tite's men are yet to hit full stride at Russia 2018, and on this evidence they still have more to come, but Neymar's 51st-minute goal and Firmino's tap-in after coming off the bench meant the tournament favourites progressed with relative comfort in the end, and avoided the early exit that has already befallen the likes of Spain, Germany and Argentina.
Mexico were the dominant force in the opening 20 minutes in Samara, but they were unable to make their superiority count and eventually allowed their muted opponents to scrap their way into the game.
After Mexican goalkeeper Guillermo Ochoa had been called into action to deny Gabriel Jesus and Philippe Coutinho, Neymar finally made the breakthrough at the back post - netting his second goal of the tournament shortly after half-time, when Willian's scuffed cross found its way through to him.
The margin became more comfortable with two minutes left when Firmino - just on as a replacement for Coutinho - added the finishing touch after Neymar had led a counter-attack.
The only blemish for the five-time champions was the second-half booking for Casemiro, which rules him out of the quarter-final clash against either Belgium or Japan.
Mexico, meanwhile, will look back fondly on their opening 1-0 win over Germany, but are now left to rue a seventh consecutive exit at the last-16 stage.
#BRA get the job done!
— FIFA World Cup (@FIFAWorldCup) July 2, 2018
In a lively start, both sides exchanged chances inside the opening five minutes. Hirving Lozano's half-volley was well blocked by Miranda, while at the other end, Ochoa was equal to Neymar's powerful drive from just outside the penalty area.
Lozano was to prove a constant menace down Mexico's right, with only a Filipe Luis block preventing him from providing the final flourish to a flowing counter-attack.
Neymar cut an isolated figure during Brazil's disjointed start, but he exploded into life after 25 minutes, racing past Edson Alvarez in the area and forcing Ochoa into a smart save with his left hand.
Buoyed by that sorely-needed injection of dynamism, Tite's men then carved out two quick-fire chances. First, Jesus scuffed his close-range volley wide, and then Coutinho flashed an effort well over from 20 yards out.
Jesus went close again in the 33rd minute, finding space in a crowded area and drilling in a left-footed strike that Ochoa palmed away.
Brazil picked up where they had left off after the restart, Coutinho testing Ochoa with a fierce drive after cutting in from the left.
And their positive approach was rewarded in the 51st minute as Neymar and Willian combined to devastating effect.
6 - Neymar has scored six goals from 38 shots in World Cup tournaments - it took Lionel Messi 67 shots and Cristiano Ronaldo 74 shots to reach this goal tally at the World Cup. Icon. #BRA #MEX #BRAMEX #WorldCup pic.twitter.com/RiSPxMgzja
— OptaJoe (@OptaJoe) July 2, 2018
Neymar's back-heel on the edge of the area teed up the Chelsea man for a burst into the box and his scuffed cross was slid into an empty net by the Paris Saint-Germain forward, who had ghosted in unmarked at the back post.
Paulinho should have doubled that advantage in the 59th minute, but Ochoa was once again equal to his whipped strike from 12 yards, while the over-worked goalkeeper also tipped over Willian's powerful effort four minutes later.
Substitute Miguel Layun was fortunate to escape punishment when he appeared to stand on Neymar's leg 20 minutes from time as the two clashed on the touchline, although the Brazil man's histrionics did not help his cause in convincing referee Gianluca Rocchi to brandish a card.
As Mexico threw bodies forward in search of a late leveller, Brazil took full advantage of the gaps in their backline to score a second with two minutes remaining.
Neymar powered through and his low effort was diverted by Ochoa's foot into the path of Firmino, who had the simple task of tapping into an empty net.
After their slow start it was ultimately no more than the Selecao deserved, as their bid for a sixth world title marches on.
Photo Getty Images. Caption: Brazil's Neymar