Atletico had chances to kill the game before half-time as Luciano Vietto and Antoine Griezmann missed one-on-ones with Jeroen Zoet.
The hosts had to resist for the final 20 minutes a man light when Gaston Pereiro saw red for a second bookable offence.
However, Atletico failed to take advantage meaning all is to play for when the sides meet again on March 15 at the Vicente Calderon for a place in the last eight.
“From the start of the game we pressed them, played in their half and created chances,” Atletico manager Diego Simeone told beIN Sports.
“In the second half we controlled the game and (Jan) Oblak didn’t have a save to make, so I am very happy with the team.”
And despite his side’s struggles to score goals of late, Simeone is confident their excellent home record in Europe will see Atletico into the quarter-finals for a third consecutive year.
“I don’t like to lie and I speak honestly. Playing at home (to decide the tie), how can I not be calm?”
Vietto was handed a start ahead of Fernando Torres as Griezmann’s strike partner and should have opened the scoring after just three minutes.
Gabi’s long ball through the middle caught the PSV defence flat-footed and the Argentine lifted the ball over the advancing Zoet, but Jeffrey Bruma got back just in time to clear the ball off the line.
PSV had seen off Manchester United in the group stage to reach the last 16 for the first time in nine years and showed signs they could produce another upset during the first half.
The home fans and coach Phillip Cocu were furious when Jurgen Locadia went down under Gabi’s challenge inside the area, but referee Daniele Orsato was unmoved.
Yet, Atletico were constantly finding space in behind the Dutch champions’ defence and Koke was next to have a go at chipping the ball over Zoet but didn’t get enough on his effort to beat the keeper.
Griezmann then had the best chance of the game when he raced onto Koke’s through ball to beat the offside trap, but Zoet rushed from his line to make a vital save.
PSV could even have been in front before half-time when Davy Propper shot straight at Jan Oblak from close range after great work by Pereiro.
Chances were harder to come by in the second period as neither side ran the risk of conceding the winner.
Diego Godin did have the ball in the net just after the hour mark, but his header from Koke’s corner was rightly ruled out for a foul on Hector Moreno.
PSV were then forced to try and see out the final 20 minutes when Pereiro picked up an unnecessary second booking for a flying elbow on Godin.
Torres had been introduced just before the dismissal for Vietto in the search for an away goal, but he wasted Atletico’s best chance against the 10 men as he blazed well over from Juanfran’s intelligent cut-back.
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