Juventus took the lead on the stroke of halftime as Portuguese forward Ronaldo began an attacking move inside his own half.
He then sprinted 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.
The Ajax player then 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.
Hakim Ziyech had several efforts at goal in a lively start for the youthful Dutch team, who have come through the pre-group phase qualifying round to reach the last eight.
Donny van de Beek scraped the outside of the upright with a 25th minute effort from close range after opening up space for himself in the penalty area in Ajax’s best chance of the first half.
But Juventus, with the 34-year-old Ronaldo central to their attacks, worked their way into the contest and came close themselves.
Ronaldo set up Federico Bernardeschi to turn and shoot in the 37th minute. But he was just off target.
Ronaldo, who scored a hat-trick in the previous round against Atletico Madrid, then scored a 125th Champions League goal.
After equalising, Ajax then dominated possession but were guilty of over-elaborate passing and were also fortunate not to have given away a penalty.
Defender Nicolas Tagliafico was tugging on the jersey of Juventus captain Mario Mandzukic and was lucky not to be punished.
Spanish referee Carlos del Cerro Grande paused briefly in the 53rd minute to presumably hear from the Video Assistant Referee (VAR) but resumed play before TV replays showed that Juventus had been denied a decent claim.
Juve hit the upright in the closing stages through substitute Douglas Costa although Ajax could have had the last say as Dusan Tadic missed a good chance in stoppage time.
More than 100 Juventus supporters were detained by Dutch police before the match while home fans were also arrested as a water cannon was used outside the ground.