It was a choking blow for Mexico, who had been the better side for the opening half an hour, pegging Brazil back and creating several half chances.
With Messi and Ronaldo having packed their bags, Neymar is the final superstar remaining the World Cup.
Jesus, 21, has yet to score on his World Cup debut.
Brazil will now face the winners of Belgium and Japan in the quarterfinals, though Casemiro will be suspended after picking up a yellow card in the second half.
The game in Samara, Russia, kicked off in sweltering 92-degree temperatures, making it as much a struggle for survival as it was a soccer match.
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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.
The Brazil forward slid toward goal and tapped in after Willian sprinted down the left and fired in a low cross.
Jesus then had another opportunity as a nervous Mexico defence failed to clear, but the Manchester City striker found Ochoa equal to his shot.
Neymar's strike and a late second from Roberto Firmino saw a strangely low-key Brazil edge past Mexico 2-0 to book a spot in the World Cup quarter-finals.
With 20 minutes left to play, Mexico's Miguel Layun stepped on Neymar's balky ankle.
He wouldn't be called on to make another as Brazil posted its third consecutive shutout, running its scoreless streak to 310 minutes.