Leading 3-2 after last week's first leg, they wrapped up an aggregate 4-2 victory on Tuesday night courtesy of Karim Benzema's 72nd-minute goal.
Alvaro Arbeloa was dismissed for Jose Mourinho's men, who will face the winners of Thursday's return between Osasuna and Barcelona, which the European champions lead after a 4-0 first leg success at the Nou Camp last week.
"We've scored eight goals in our previous two games and people accused us of not defending well. We gave a serious, pragmatic and practical performance tonight. We defended very well and our opponent hardly had any chances to score," said Mourinho.
"We didn't give a brilliant performance with the ball, but we never the less reached the next round against a solid side that played intelligently in both legs. It would have been even harder if we hadn't scored the goal. We made a great effort to win."