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.
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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).
'World-class goal from world-class players' puts Madrid through
Holding a slender lead thanks to Brahim Diaz's superb winner in the first leg, there was an expectation on Real to demonstrate their quality and experience to see the job through on home turf.
Ancelotti was keen to make clear that the tie was far from over, reinforcing the point during his pre-match news conference to ensure there was no complacency among his ranks.
But his side responded with a subdued performance and, judging on the balance of play in both matches, were rather fortunate to progress.
Real did not register an effort on target in the first half and continued to lack ideas after the break.
Whistles from the Bernabeu stands when Leipzig had possession indicated the concern of the home fans and their exasperation grew as Real continued to cheaply give away possession.
However, they possess a wealth of devastating attacking talent - led by Brazil forward Vinicius and England midfielder Bellingham - and the home side eventually clicked into gear.
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Germany midfield maestro Toni Kroos won back possession on the edge of his own penalty area, using his speed of mind to set Bellingham away on the counter attack - and that was ominous for Leipzig.
Bellingham confidently strode forward before picking out the run of Vinicius, who intelligently cut inside from the left into a central area and sweetly drove a rising shot into the top corner.
One flash of brilliance, like it did in the first leg in Germany, proved enough for the Spanish side but they know a better performance will be required whoever they face in the quarter-finals.
"It is a world-class goal from world-class players. Madrid were bang average in the two games. But world-class players can win matches in the blink of an eye," former England midfielder Owen Hargreaves said on TNT Sports.
The home side were penned back by Leipzig for a significant portion of the game, conceding 20 shots at their goal as the visitors showed fearlessness and bravery in front of 80,000 fans at the recently-renovated Bernabeu.
The clearest chances fell to Belgium striker Lois Openda but his lack of composure in threatening areas stopped Leipzig levelling the tie, which would have given them a platform to try and win it.
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Instead the late onslaught proved too little too late. Ultimately, the efforts of the 2019-20 semi-finalists were fruitless as they failed to go beyond the last 16 for the fourth successive season.