The two Spanish giants came into the second leg at the Santiago Bernabeu, with the tie delicately poised at 1-1,
The hosts dominated in the first half, but Vinicius Junior wasted two good chances.
Madrid started strongly in the second half before Suarez converted Ousmane Dembele’s pass. Raphael Varane was forced the ball past his own keeper under pressure.
Suarez rounded off rounding from the penalty spot, after being fouled by Casemiro.
Barcelona, who have won the competition four years running, will face Real Betis or Valencia in the final.