A fine David Neres goal cancelled out Cristiano Ronaldo's header to leave this tie delicately poised heading to Turin.
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Ajax and Juventus head to Italy all-square after an entertaining quarter-final first leg at the Johan Cruijff ArenA.
Wojciech Szczęsny had to be at his best to keep out Hakim Ziyech's drive while Donny van de Beek drilled wide as the hosts impressed early on, but Juventus made the breakthrough on the stroke of half-time when Cristiano Ronaldo headed in João Cancelo's cross.
Ajax levelled inside the opening minute of the second half as David Neres curled a wonderful effort past Szczęsny after dispossessing João Cancelo. They were the driving force thereafter but were very nearly caught out late on when Douglas Costa's strike cannoned back off the post.
View from the stadium: Derek Brookman
Ajax's European adventure continues with another thrilling performance against top-quality opposition. In a vibrant Johan Cruijff ArenA, the Amsterdammers were more than a match for the record Italian champions, and with a little more accuracy in their finishing could have recorded a victory. Frenkie de Jong and Neres were particularly outstanding, although the entire team did themselves proud. All to play for in Turin!
Man of the match: Frenkie de Jong
The 'brain' of this exciting Ajax side played every ball with his unique elegance. He always seems to know exactly what do well before receiving the ball and directs the tempo of the game like an orchestra director. Enough? Certainly not. His defensive contribution was also great – just watch how he charged back and tackled to deny Federico Bernardeschi in the first half.
2: Neres has scored in successive UCL games having not found the net in his first seven.
7: Ajax have not won any of their last seven UCL knockout phase home matches (D4 L3).
8: Ronaldo has scored eight goals in his last five UCL games against Ajax.
9: All nine of Ajax's home goals in this season's UCL have been scored during the second period.
15: Ajax have lost only one of their 15 European matches in 2018/19 (W8 D6).
1969: Ajax's defeat by Benfica in 1969 is their only home European Cup quarter-final loss; their record otherwise reads W6 D6.
What does it mean?
Ajax were seeking a first win in nine games against visitors from Serie A but must now wait a while longer to end that run, while Juve are unbeaten in seven matches against Eredivisie clubs (W4 D3).
Ajax continue their intriguing battle with PSV for the Dutch title – the pair are level on points – when they host lowly Excelsior on Saturday. Juventus have no such domestic worries as they sit 20 points clear and can retain the Serie A crown with victory at SPAL on the same day. The second leg of this tie takes place on Tuesday 16 April.