Diego Costa earned his first start after a two month injury layoff, while Miralem Pjanic survived a flu scare to start for the away side.
Eight minutes into the tie, Cristiano Ronaldo drove a scorching free-kick from range which was sneaking under the crossbar had it not been for great reflexes from Jan Oblak.
Moments later, Leonardo Bonnuci has a great opportunity to score when the defender rose highest to connect with Pjanic's corner kick but couldn't trouble Oblak with a header.
The half was an intriguing tactical contest with both teams defenses working hard to close each other down.
Atletico Madrid were then awarded a penalty at the midway points, but the Video Assistant Referee (VAR) adjudged Diego Costa to have been bought down outside the box.
The half ended with Juventus having the upper hand in terms of possession however neither team could break the deadlock.
Atletico Madrid began the second half with real conviction and attacking intent, Costa was delicately played through on goal by Griezmann, but the striker did everything right but to find the target.
This time around Griezmann got to breach the Juventus defense before chipping the ball over Wojciech Szczesny which hit the crossbar as Giorgio Chiellini cleared the rebound.
In the 70th minute, The home team thought they had grabbed the lead through Alvaro Morata’s header but VAR disallowed the goal for the striker’s push on Chiellini.
The goal finally came for Atletico when Jose Gimenez fired home from close range goal after a goal-mouth scramble with 78 minutes gone.
Four minutes later, Diego Godin doubled the lead with a delightful finish that took a slight deflection off Ronaldo.
The first leg deservedly ended in favour of Atletico as Diego Simioene’s men travel to Turin for the second leg.