Juanfran slotted home the winning kick, moments after Luciano Narsingh had smashed the bar with PSV’s eighth effort.
The teams had battled to a 0-0 stalemate over 90 minutes, just as they had in the first leg in Eindhoven.
And no one could find the breakthrough in extra-time, meaning the tie was decided from the spot.
Fourteen successful penalties followed, with both Atléti’s Jan Oblak and PSV’s Jeroen Zoet struggling to get close to many attempts in what was a high-quality shootout.
Then Narsingh, introduced as a late substitute at the end of extra-time, crashed his effort on to the bar and Juanfran put Diego Simeone’s side into the quarter-finals for the third season in succession.
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