A 0-0 draw at home had built up Olimpic's hopes of an unlikely upset but Asier Illarramendi eased Real's concerns with the opening goal after 16 minutes and midway through the first half Angel Di Maria converted a penalty.
Gareth Bale was among the injured players and Cristiano Ronaldo was suspended for a game in which Real coach Carlo Ancelotti kept faith with his second string who had disappointed in the first leg.
Real reached the last 16 along with Atletico Madrid, who beat their Madrid rivals in last season's final, and won 2-1 against Sant Andreu earlier on Wednesday to advance.
Barcelona made short work of Cartagena with a 3-0 victory on Tuesday to qualify 7-1 on aggregate.
(Reporting by Tim hanlon, editing by Ed Osmond)
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