Atletico had the better chances throughout the contest, but PSV, who finished with 10 men following a 68th-minute red card for Gaston Pereiro, managed to keep a clean sheet ahead of the second leg in Madrid next month.
The visitors had a golden chance to take the lead inside four minutes when Vietto met a through-pass from his skipper Gabi - the Argentine poked the ball past PSV stopper Jeroen Zoet, but Jeffrey Bruma was back on the line to clear.
PSV's main threat in the opening 15 minutes came on the counter, but Jurgen Locadia and Guardado were both guilty of some sloppy passing in the final third as the away side enjoyed the majority of the ball.
Atletico again came close in the 18th minute when Koke advanced towards Zoet, but the Spanish international attempted to produce a chip and it turned out to be a comfortable save for the stopper.
Comfortably the clearest chance of the first 30 minutes fell to Antoine Griezmann, but the Frenchman could not beat Zoet after being put through on goal by the impressive Gabi.
Backed by a vocal home support, PSV continued to press forward in the latter stages of the first period, but Atletico's backline remained strong to leave the two teams on terms at the interval.
Atletico's first sight of goal in the second period came in the 51st minute when Juanfran delivered a cross in to Vietto, who looked favourite to turn home, but Hector Moreno came on the blind side to make a fine clearance.
Against the run of play, PSV almost had the lead just before the hour when Koke turned a low Jetro Willems cross towards his own goal, but it just drifted wide of the post, much to the Atletico midfielder's relief.
Atletico did have the ball in the back of the net in the 62nd minute when Diego Godin headed a Koke corner past Zoet, but the referee penalised the centre-back for climbing on Moreno.
The match swung in the away side's favour in the 68th minute, however, when Pereiro was handed a second yellow card for a high challenge on Godin. Atletico had two chances in quick succession following the red, but Gabi's strike was saved by Zoet, before Fernando Torres fired over from inside the box.
Torres remained a threat for the visitors and again came close 10 minutes from time after turning outside the PSV box, but his final effort was deflected wide by Bruma.
Another of Atletico's substitutes Angel Correa came close in the 83rd minute after turning away from Bruma, but Zoet jumped on the ball to bring more cheers from the home supporters.
PSV so nearly scored in the 88th minute when Jorrit Hendrix picked out Maxime Lestienne with a cross, but the on-loan midfielder's volley was always rising over the crossbar as it finished goalless on the night.