A first half of few chances turned into a far more entertaining second as the 2018 finalists pushed for a late winner but failed to break down a stubborn and well-drilled Morocco.
Croatia will now turn their attentions to their game against Canada on Sunday, when Morocco will face Belgium.
Croatia's best moments predictably hinged on Luka Modric, who was given the freedom of the park, floating effortlessly from back to front, with football's traditional midfield roles seeming not to apply to Croatia's captain.
One minute he was patrolling in front of his back four, the next hanging off the shoulder of Andrej Kramaric up front, but always looking to open up the north Africans, whether he was hovering at right back or hunting further forward.
Morocco looked principally to Hakim Ziyech for inspiration and the Chelsea winger, recalled to the squad following coach Walid Regragui's appointment, was their most dangerous attacking outlet in the early stages, although his good work lacked an end product.
While the encounter was low on action it was at least high on intensity, as both sides battled for midfield supremacy, but the first half ended with neither goal really threatened until the closing moments when Vlasic's low effort was saved by Yassine Bounou.
There was more action in the first five minutes of the second half when Morocco had raucous appeals for a penalty waved away after Sofiane Boufal's shot appeared to hit Dejan Lovren's arm, seconds before Mazraoui's header was saved by Dominik Livakovic.
Moments later, Lovren's effort on the slide at the other end was blocked by Sofyan Amrabat, but that was about as good as it got for Croatia until centre back Josko Gvardiol's header went wide in the 80th minute.
Additional reporting by Reuters.