The Barcelona star came to the rescue after the host nation had fallen behind at the Arena de Sao Paulo on Thursday night
The host nation fell behind to an early own goal from Marcelo, before Neymar was perhaps fortunate to be shown just a yellow card after catching Luka Modric in the throat with a stray arm.
Soon after, the 22-year-old levelled with a fine 25-yard effort on his left foot, before converting a controversial second half penalty after Dejan Lovren was adjudged to have brought down Fred.
And as the game entered injury-time, man-of-the-match Oscar sped forward and toe-poked home an effort from the edge of the box to give Brazil breathing space and, most importantly, three points.
While Brazil had the luxury of naming the same side that started last year's Confederations Cup final success over Spain, Croatia were without suspended striker Mario Mandzukic, leaving Nikica Jelavic to lead the line in his absence.
Also without injured left-back Danijel Pranjic, Croatia fired the first shot in anger as Mateo Kovacic steered an effort wide in the first minute.
Brazil's first significant foray forward saw David Luiz's tame header saved, but the pressure was on them at the other end of the pitch.
Ivica Olic's header wide served as a warning for Brazil, and it was one they did not heed, as Croatia claimed a surprise 11th-minute lead.
Olic galloped down the left wing in space before crossing for Jelavic, and although he could only scuff a left-foot shot, his effort was inadvertently steered in by Marcelo from six yards.
Brazil's initial response was frantic and anxious, but they soon found their rhythm, with Neymar's run to the byline and subsequent centre causing panic, and almost the equaliser, as Oscar saw a 20-yard left-foot effort superbly saved by Pletikosa after Croatia failed to clear their lines.
Neymar's contact with Modric then drew an angry response, with replays showing that the Barcelona star had caught the midfielder in the throat with a stray arm, before Jelavic headed straight at Brazil goalkeeper Julio Cesar.
Croatia's promising start was undone in the 29th minute, though, as Oscar, who did superbly in a cluster of players to find Neymar, watched his team-mate trickle a left-foot strike past Pletikosa and in off the inside of the post from 25 yards.
A lull was inevitable following half an hour of mayhem, but it lasted longer than expected, and although Brazil shaded the early stages of the second half, the best they had to show for it was a Dani Alves free-kick that sailed over.
That was until Nishimura pointed to the spot after Oscar's ball to Fred brought about slight contact from Lovren.
Neymar's stuttering run-up was far from convincing, and his tame effort ought to have been kept out by Pletikosa, but the goalkeeper could only get a hand to the shot on its way into the net.
A sublime Oscar cross nearly brought about Brazil's third goal, only for Luiz to head over, while at the other end Croatia's hard luck was summed up by Ivan Perisic's disallowed goal, ruled out because of Olic's minimal contact with Cesar.
Modric and Vedran Corluka both went close as well, as Croatia mounted a late charge, but Oscar's composed finish capped a stunning performance from the midfielder, as the hosts opened the World Cup with a victory.