Gareth Bale had a poor seaon and was also targeted by fans as he was booed and jeered recently.
Juventus will face Barcelona in the final, which will be played in Berlin on June 6.
Defensive lapses have cost Madrid in recent weeks as they have conceded twice in four of their last five matches.
The pressure was on Ancelotti’s men after Barcelona had mauled Getafe 6-0 on Tuesday.
It was a high-scoring thriller but Madrid managed to hang on to their lead till the referee’s whistle.
Slovenian Oblak made a string of memorable saves to keep the Spanish champions’ hopes of reaching the last four alive.
Real Madrid’s 3-0 win over Eibar earlier in the day means the European champions now trail Barca by just two points.
Rodriguez, sustained the injury in the league game against Sevilla in early February.
Bale struck a brace to end his drought and Real Madrid’s winless run with a 2-0 victory over Levante.
Real Madrid survived a major scare as they went through to the quarter-finals despite a 4-3 loss to Schalke at home.
Spanish league leaders Real Madrid lost 1-0 at Athletic Bilbao on Saturday, stumbling for a second straight week.
Real Madrid stumbled to a costly 1-1 draw with Villarreal at home on Sunday to tighten the La Liga title race.
Cristiano Ronaldo and Karim Benzema scored to give Real Madrid a 2-0 win at Elche on Sunday.
The world player of the year headed in after 26 minutes for his 73rd Champions League goal .
Real Madrid needed goals from Isoand Karim Benzema to beat a determined Deportivo La Coruna outfit.