Serbia international Vlahovic joined the Bianconeri in January from rivals Fiorentina after a sensational 18 months and showed his worth on Europe's biggest stage as he opened the scoring within 32 seconds.
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The opening goal ha Juve in control as they kept Villarreal at arm's length for the majority of the match as Arnaut Danjuma went closest for the hosts when his improvised backheel was saved by Wojciech Szczesny.
McKennie went close to adding a second for Juve on 38 minutes but saw his effort blocked by Villarreal defender Raul Albiol.
Unai Emery's side pulled a goal back through Parejo and then looked to be the more likely to take the lead as they grew in belief.
Adrien Rabiot was lucky stay on the field as he picked up just a yellow card for a shocking challenge on Samuel Chukwueze on 73 minutes while McKennie was forced off with an ankle injury on eight minutes later. After the match, multiple sources with direct knowledge of McKennie's injury confirmed to ESPN that the midfielder suffered fractures to the second and third metatarsals in his left foot, which will leave him sidelined for 8-12 weeks.
Speaking after the draw, Vlahovic said he was happy with his goal but disappointed not to get the win.
"My dream has come true at Juve, but I am not happy because we didn't win and we all really wanted the victory today," Vlahovic told Mediaset. "It didn't happen, so we move forward.
"I think we did what we had prepared in the locker room, but of course a lot depends on the opponents. We say congratulations to Villarreal on their performance, we tried to continue the way we started.
"I have personally already forgotten this match, we just have to look forward to the next game."
The return leg will take place on March 16 at Juve's Allianz Stadium.