The world's most expensive player put Brazil in the lead after his back-heel released Willian, who then sent the ball into the penalty area.
After a scoreless first half, El Tri conceded its first goal in the 51st minute of the match before Brazil scored again in the 88th minute, ensuring that there would be no way for Mexico to force a draw and extend the match into extra time.
Brazil coach Tite was unsurprisingly supportive of Neymar, dismissing accusations of playacting, while preferring to talk about his improving side, who seem to be finding their rhythm after a third successive 2-0 victory.
French footballing legend Eric Cantona has delivered a hilarious smack-down on Neymar, who has been widely condemned by fans for his play-acting in the World Cup win against Mexico. It turned out to be pure histrionics.
Brazil will face the victor of Belgium-Japan on Friday in the quarterfinals.
Not so for the Mexicans, who have lost in the round of 16 seven straight times. Defending champion Germany arrived with 224 total.
"We wasted a lot of time because of one single player", Mexico coach Juan Carlos Osorio said, without naming Neymar. Check out some of the best reactions to Neymar's rolling antics below.
Mexico'sWorld Cup run has come to an end.
"It was unfair. The ball was not in play and we were off the pitch", he signalled.
During the group stage, Neymar was often guilty of trying to go it alone, reminiscent of the 2014 World Cup in which he represented the Selecao's sole hope of winning the tournament.
Another added: "It's either watching dolphins flop around at SeaWorld or watching Brazil play".
"I think it had an impact on our pace", said Osorio of the stoppage that arose from the Neymar-Layun incident.
With Brazil squeezing Mexico, the PSG striker made the breakthrough in the 50th minute, exchanging an elongated one-two with Willian before latching onto a low cross to slide home from close range... Fresh among tiring legs, Firmino was able to evade the defence to get in the right place to score the second goal. Upsets in this tournament have already claimed the last two World Cup finalists and the last two World Cup winners.
Brazil will take on Belgium in a mouth-watering quarter-final encounter on Friday.
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Collins said she suggested he add some names, and that the White House counsel told her some names have been added. Wade . "I believe that is a very important, fundamental tenet to our judicial system".