Another South American rival awaited at the quarter-final juncture, with Luiz's outstanding 35-yard free-kick decisive in a 2-1 victory after which one of the main talking points will be Neymar's fitness.
The 22-year-old, so key to the Selecao, went to ground in agony during the closing stages after taking a knee to the back from Juan Zuniga, leaving the field in tears on a stretcher.
54 - A total of 54 fouls were committed in #BravsCol tonight, the most in any game at this World Cup so far. Feisty.
Brazil will be sweating on their star man's fitness ahead of their semi-final against Germany, which captain Thiago Silva will definitely miss after incurring a suspension for his booking at the Estadio Castelao.
The skipper played a key role in the Selecao's progression in Fortaleza, though, defending resolutely after opening the scoring inside seven minutes.
It was a lead Brazil worked hard to extend and, having seen a Mario Yepes goal ruled out for offside, struck with aplomb midway through the second half, with Luiz sending home an outstanding 35-yard free-kick to send the nation into delirium.
James Rodriguez, the competition's top scorer, added to his haul with a penalty but Brazil rode out a nervy final 10 minutes to progress, with attentions now undoubtedly turning to the fitness of Neymar.