Either side had changes in goal, as Everton turned to Joao Virginia to replace the injured Jordan Pickford whereas the Citizens recalled Zack Steffen and hauled back Raheem Sterling.
An open affair from the respective sides provided openings for amongst others Oleksandr Zinchenko on the side of City and Dominic Calvert-Lewin, but neither profited.
Sterling put the Toffees on the back-foot shortly before the midway stage with a low shot outside the area following an exchange of passes with Ilkay Gundogan, but Virginia smothered.
The Citizens entered the second half eager to exert their dominance from the first spell even further, as Sterling drilled a ball from outside the area by Zinchenko over the top.
Everton were nearly sliced apart right on the 60th minute mark after Sterling fired in a first-time strike from the edge of the area, but Virginia's finger-tips denied the visitors the front-foot.
Pep Guardiola looked to the bench midway in the second half, as the breakthrough proved hard to come by and introduced Riyad Mahrez in the place of Bernardo Silva.
The Algerian international set into the action immediately when he teed-up Foden for a shot at the elusive breakthrough, but the latter blazed wide of Virginia's goal.
Everton's resistance finally came to pass five minutes before time after Gundogan headed in a rebound from the crossbar following a curling shot from Kevin De Bruyne.
De Bruyne went on to find the second in the last two minutes when he beat the offside trap to run onto a ball over the top from Rodri for a composed finish to send City to the final four.