With the hosts on a rampant hot streak - PSV won 10 of their previous 11 games and were unbeaten in 14 - Atletico Madrid ought to start brightly via Marc Pubill and Nico Gonzalez, who both couldn't find a way past Matej Kovar.
A lightning-quick counter saw PSV take an early lead not much later - Ismael Saibari launched Couhaib Driouech onto Atletico's half with a perfectly weighted deep ball, after which the Moroccan winger found a wide-open Guus Til, who only had to tap the ball into an empty goal.
The goal took the wind out of Atletico's sails as PSV continued to pile up pressure. Driouech failed to reward himself for a stellar first half, however, by firing the ball wide following one counter and inexplicably passing the ball while getting a free, unobstructed shot at goal.
Atletico Madrid picked up the pace in the final 15 minutes of the first half, putting PSV under pressure in their own half and eventually finding the equaliser via Julian Alvarez, who calmly put the ball in an empty net after PSV centre-back Yarek Gasiorowski clumsily lost possession in front of his own penalty box.
PSV lost all control over the match and nearly conceded again when Alexander Sorloth took Kovar under fire, but the Czech stopper calmly parried the ball away.
Kovar couldn't produce a save of the same quality shortly after the break when Nahuel Molina fired a shot from distance at the Czech, who couldn't parry it away safely and handed former Feyenoord captain David Hancko the chance to fire the ball home in the 52nd minute.
Atletico doubled their lead shortly after when Pablo Barrios was allowed to freely rush deep down PSV's half and deliver a perfect cross to Alexander Sorloth, who headed home uncontestedly.
PSV took over again but failed to create any big chances as the clock kept ticking for Peter Bosz's men.
American striker Ricardo Pepi handed PSV a lifeline as he made a clever run at the second post to tap in the 3-2 with five minutes remaining.
With extra time just seconds away, PSV couldn't have asked for a bigger chance when centre-half Armando Obispo got the ball served on a plate and only had to tap it in an empty net, but the Curacao international couldn't connect properly and sent the ball wide.
It proved to be the last big chance for the home side, who lost their first game in 15 tries as Atletico Madrid took home third-straight UEFA Champions League win.
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