The Bundesliga side - without star man Timo Werner - opened the scoring five minutes into the second half when Spaniard Dani Olmo headed home Marcel Sabitzer's cross.
However, Diego Simeone's team drew level thanks to substitute Joao Felix, who both won and converted a penalty with 19 minutes to go.
With extra-time looming, though, Leipzig won it thanks to their own substitute as Adams saw his low drive deflect in past a helpless Jan Oblak via Stefan Savic's outstretched leg.
Atletico may have entered this เล่นบาคาร่ามือถือ last-eight showdown at the Estadio Jose Alvalade as favourites after eliminating holders Liverpool in the previous round, but it was their opponents who made the more assured start in the Portuguese capital, with defender Marcel Halstenberg wasting a good early opening when blasting over from close range.
Gradually, though, Atleti gained a foothold in the contest, with Yannick Carrasco - back at the club after a two-year stint in China - testing Peter Gulacsi at his near post with a fierce drive.
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