Juventus took the lead on the stroke of halftime as Portuguese forward Ronaldo began an attacking move inside his own half before sprinting down field and diving to head in a clever chip from Joao Cancelo.
Ajax equalised 30 seconds into the second half after Cancelo lost control of the ball to allow David Neres to run down the left wing, cut inside and curl the ball past Juve goalkeeper Wojciech Szczesny.
The result leaves the Serie A side in a strong position to advance to the semi-finals in next week's return leg in Turin. However, they will be mindful of Ajax's 4-1 away win over Real Madrid in the last round that eliminated the holders 5-3 on aggregate.