The tense quarter-final encounter in San Juan featured extra-time goals and two penalty shots wasted by Israel, who will face Uruguay or the United States in the semi-finals.
After a scoreless first half, Marcos Leonardo netted first and Israel equalised with a header by Anan Khalaili four minutes later.
Matheus Nascimento made it 2-1 for Brazil in the first minute of extra time, but Hamza Shibi scored Israel's second two minutes later from close range.
Dor David Turgeman scored the winner in the third minute of the second half of extra time after dribbling past two Brazilian defenders in the penalty box.
Israel squandered two penalty kicks in the second half of extra time, which drew out the drama to fulltime.
"Israel was better than Brazil, we didn't play our best match," said midfielder Marlon Gomes, who played extra time while injured because Brazil couldn't make substitutions.
"We couldn't hold our lead in two different opportunities. We could have done better."
Hours later, Italy did not suffer as much as they overcame Colombia 3-0 to advance.Â
Cesare Casadei, one of the top players of the tournament, scored with a header in the 9th minute. Tommaso Baldanzi added a second from close range in the 38th minute. Francesco Esposito made it 3-0 in the 46th minute.
Colombia reduced their deficit with a Jhojan Torres goal in the 49th minute from the edge of the box.
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