Los Blancos entered the match holding a 3-0 advantage from the first leg of their quarter-final in Turin, but Juventus hit back with three goals of their own to leave the tie level at 3-3 entering stoppage time at the end of the 90 minutes.
Cristiano Ronaldo spectacularly sent the Spanish side into the final four, however, when he converted from the penalty spot after Medhi Benatia had felled Lucas Vazquez, with the aftermath seeing Juventus goalkeeper Gianluigi Buffon receive a straight red card for dissent.
"We put our necks on the line and gave everything to go through," Marca quotes Marcelo as saying. "The penalty? It was very clear. What happened to Barcelona wasn't going to happen to us because we're Real Madrid."
Madrid are bidding to win the Champions League for the third season in a row.