Vinicius Junior scored an equalising goal in the 32nd minute, giving five-time champions Brazil a share of the points on Saturday (Sunday AEST) in a pulsating, high-profile group match.
"We started on a really bad note," Vinicius said. "For certain, we've got to hold on to the ball. We have to move better."
Semi-finalists four years ago, Morocco took control and Ismael Saibari put the African champions ahead in the 21st minute with a superb goal.
Brazil evened the score 11 minutes later after Vinicius exchanged passes with Bruno Guimaraes on the left flank, took touches to make space and rifled a right-footed shot past the outstretched arm of Yassine Bounou for his 10th international goal.
Brazil, seeking their first World Cup title since 2002, entered the tournament with high expectations and yellow-clad Selecao fans who dominated the crowd of 80,663 at MetLife Stadium became a bit subdued before Vinicius evened the score with his spectacular angled effort.
"The team was a bit anxious at the beginning. Nerves were all over the place," Brazil coach Carlo Ancelotti said. "A very imbalanced team."
World no.6 Brazil and seventh-ranked Morocco are the only top 10 teams to meet in the first round of the expanded 48-nation World Cup tournament.
"We cannot lose heart," Ancelotti added. "You don't win a World Cup based on your first match."
Despite shaky moments, Brazil managed to extend their unbeaten streak in World Cup openers to 21, including 17 wins, since a 1934 loss to Spain.
Brazil play Haiti on Friday in Philadelphia, then close Group C against Scotland in Miami Gardens, Florida.Â
Morocco face Scotland in Foxborough, Massachusetts, on Friday, then meet Haiti in Atlanta.
Brazil star Neymar, recovering from a torn right calf, didn't dress for the game.
Morocco went ahead after Lucas Paqueta lost control of a short pass from Roger Ibanez and knocked it off Bilal El Khannouss. It bounced to Noussair Mazraoui, who sent the ball to Brahim Diaz in the center circle.
His long through pass split Gabriel Magalhaes and Marquinho, and Saibari ran onto the ball at the top of the arc. Alisson Becker was slow to come off his line and Saibari chipped the ball over the Brazil goalkeeper for his 10th international goal.
"We are satisfied with the draw," Morocco coach Mohamed Ouahbi said. "We are not euphoric."
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