The Chelsea forward's low driven cross across the six-yard box was touched home from close range by Neymar for his 57th worldwide goal.
Replays showed that Layun did in fact step on Neymar's leg, but his exaggerated reaction after the foul was something to behold.
The star forward opened the scoring early in the second half at the Samara Arena and it was his shot being saved which led to Roberto Firmino's 88th-minute clincher.
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The Mexico captain, at 39 years and 139 days, had become the oldest outfield player to start a World Cup knockout match since Stanley Matthews in 1954 for England against Uruguay.
It was the seventh World Cup running that Brazil have reached the last eight, where they will now face Belgium or Japan, while Mexico have not made it to that stage since they hosted the tournament in 1986.
Brazil endured a frustrating opening 45 minutes as they head into the halftime break with the score level at 0-0 against Mexico in their round of 16 tie. He now has six goals at the World Cup and 57 in 89 total appearances.
For Brazil Neymar had an effort palmed away by the outstanding Guillermo Ochoa. If Neymar and rising hero Philippe Coutinho are to advance, they'll have to take on a tough Mexican squad with some notable names of their own.
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Brazil will now face the victor of the match between Belgium and Japan.
His run across goal and clever backheel won Willian space, and the Chelsea midfielder only needed two touches to drive into box and lay the ball across for the world's most expensive player to slide home.
"When you compare the possession against Brazil we had 53 percent against 47 percent, it looked to me the game was very even and it was decided in the penalty area", he added.
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Deschamps expects more from the 27-year-old, and said: "He's had a hard start. the France team needs Antoine Griezmann to be at his best level, and I hope tomorrow that will be the case".