Yousseff En-Nesyri was the hero as his first half goal was enough to end Portugal’s run.
It is the second time Morocco will overcome Portugal at the World Cup after first beating the 2016 European champions 3-1 in the group stage at the Mexico 1986 edition.
The Portuguese edged Morocco 1-0 when they two teams met in Russia 2018.
Morocco will now face either reigning champions France or England in the semi-finals.
Portugal got the first attempt on goal in the 5th minute through Joao Felix but his header was turned around the post by the Moroccan keeper.
In the 18th minute Hakim Ziyech cut inside and shot but it rolled harmlessly wide of Diogo Costa’s goal.
On the half hour Felix’s shot from the edge of the box got a big deflection and landEd on the roof of the net.
But in the 42nd minute it was Morocco who went 1-0 up thanks to En-Nesyri.
The Moroccan forward beat the Portuguese keeper who came out to claim a cross from Attiyatt Allah but missed.
Allah could have doubled Morocco’s following a break but failed to direct his shot towards goal with the keeper to beat.
Just four minutes into the second half Jawad El Yamiq almost doubled Morocco’s lead after meeting Ziyech’s free kick but Diogo Costa made a great reflex save.
On 58 minutes Goncalo Ramos had a great chance to equalize as he met a cross but headed just wide inside the box.
Manchester United star Bruno Fernandes went close on 63 minutes but fired a shot just over the crossbar.
In the 83rd minute Felix hit a sweet left foot strike but the Moroccan keeper tipped it over the bar.
Few minutes later Cristiano Ronaldo connect to a pass but saw his shot well saved.
With two minutes left in added time Pepe headed a cross from Raphael Leao but saw his effort narrowly miss the target.
On 93rd minute Morocco were reduced to 10 men after Walid Cheddira was sent off.