Substitute Soufiane Rahimi scored 12 minutes from time on Wednesday (Thursday AEST) in Atlanta to put them ahead after Haiti had twice taken the lead in the first half, Gessime Yassine adding a fourth late on.
Haiti stunned Morocco after 10 minutes with their first World Cup goal in 18,994 days, Lenny Joseph's neat flick from a cross from Danley Jean Jacques going in off goalkeeper Yassine Bounou, who was credited with the own goal.
Bounou's opposite number Johny Placide made a double save from Achraf Hakimi and Ayoub El Kaabi, but was powerless to stop Hakimi bundling in the equaliser after 38 minutes off his standing leg after the goalkeeper had palmed a cross across the goal.
They remained level for just four minutes, Sunderland striker Wilson Isidor finding the top corner with a stunning strike from 25 yards.
But Morocco, beaten semi-finalists in Qatar four years ago, were back level before the break, Saibari's strike from outside the box after Hakimi's cut back, leaving Placide with no chance.
Haiti defender Ricardo Ade narrowly cleared his own bar from the edge of the box and made a vital interception as they were caught out on the break, but from the resultant corner Soufiane Rahimi's smart first touch allowed him to fire into the top corner via a deflection off Ade.
Yassine added the fourth with the ball judged not to have fully crossed the byline before Rahimi's cross.
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