Juanfran converted the winning spotkick at the Vicente Calderon Stadium, before ripping off his shirt and charging to celebrate wildly with the home fans after the two sides became the first to end a Champions League knockout match 0-0 on aggregate.
It took 16 kicks to finally produce a winner with Luciano Narsingh hitting the crossbar with PSV's eighth effort before Juanfran coolly delivered for his side. Atletico are into the last eight for third successive year, having also needed penalties to beat Bayer Leverkusen last season.
The Spanish side, runners-up in 2014, had home advantage in Tuesday’s second leg after drawing in the Netherlands but were kept in check by a disciplined defensive display from the Dutch champions.
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Atletico should have gone ahead after 15 minutes when Koke set up Antoine Griezmann, but PSV goalkeeper Jeroen Zoet blocked his low shot with a fine reflex save from 10 metres.
Zoet denied Griezmann again when he beat away the Atletico forward's goal-bound header from point-blank range in a first half of few chances.
PSV looked for opportunities on the counter-attack and Luuk de Jong missed a chance for the Dutch champions just before the break.
PSV were more adventurous in the second half, however, and came closest to breaking the deadlock in the 58th minute when Jurgen Locadia’s shot from the left was pushed onto the post by Atletico goalkeeper Jan Oblak.
Atletico defender Filipe Luis then reacted quickly to prevent De Jong from scoring on the rebound.
Just after the hour mark, Zoet blocked an effort from Filipe Luis and the rebound fell for Yannick Carrasco, who shot wildly over the bar.
Substitute Fernando Torres led Atletico’s attacking efforts in the second half spurning two half-chances before he had a firm left-footed shot from an acute angle palmed onto the crossbar by Zoet in the 87th minute.
Lucas Hernandez headed over in extra time after finding himself unmarked from a corner and Atletico captain Gabi wasted a free kick on the edge of the PSV penalty area, but the hosts could not find a way through.
(Reporting by Mark Gleeson; Editing by Toby Davis)
