Real Madrid reached the Champions League quarter-finals as Vinicius Junior provided the quality finish that RB Leipzig lacked to secure a 2-1 aggregate win in the last 16.
Like the first leg, German side Leipzig were made to pay for wasting a host of chances when Vinicius clipped in Jude Bellingham's pass with 25 minutes left for a 2-0 lead.
Leipzig finally converted an opportunity three minutes later when skipper Willi Orban flicked in a header.
The goal provided renewed belief to the Bundesliga side and they continued to open up the Spanish league leaders as they searched for a leveller.
Former Barcelona youngster Dani Olmo came the closest to taking the tie into extra time - because away goals no longer count in Uefa competitions - when his looping header clipped the top of the crossbar in injury time.
But Real, aiming to become European champions for a record-extending 15th time, managed to hold out and reach the quarter-finals for the 12th time in the past 14 seasons.
Carlo Ancelotti's side will find out their quarter-finals opponents when the draw for the last eight is made on Friday, 15 March (11:00 GMT).