Ronaldo – fit to feature after recovering from a thigh injury suffered on international duty with Portugal last month – put the visitors ahead on the stroke of half-time, striding into the penalty area before throwing himself at a cross to thunder a header beyond goalkeeper Andre Onana.
That lead lasted less than a minute of the second period, however, as Neres curled home his third Champions League goal of the campaign – a leveller that was the very least Erik ten Hag's side deserved for a display full of energy and attacking intent.
Donny van de Beek and Hakim Ziyech will reflect on missed opportunities that could have given the Eredivisie side an advantage ahead of the return fixture in Italy, though Juve could have snatched an undeserved win in the closing stages when substitute Douglas Costa hit the post.
Both sides went close inside the opening six minutes, Federico Bernardeschi fizzing narrowly over for the visitors and Ziyech crashing into the side netting with a fierce left-foot drive.
Ziyech then forced Wojciech Szczesny into a smart save to keep out his curling effort from 15 yards, while an unmarked Van de Beek inexplicably whipped wide from the same distance after 25 minutes.
Bernardeschi again came close nine minutes before the interval, swivelling and firing wide from Ronaldo's knock down, before the Champions League's all-time top goalscorer plundered his 125th in the competition, converting Joao Cancelo's lofted ball into the area with a thumping finish.
The hosts stormed out at the start of the second period and were level within 30 seconds, Neres cutting inside Cancelo and bending a wonderful strike into Szczesny's left-hand corner.
Ajax utterly dominated after that – coming close through Jurgen Ekkelenkamp's low effort – but never scored the second that would have made their task next week a little easier.
What does it mean? Ajax left to rue missed chances
Juventus were well off the pace and Ajax will be hoping that their squandered chances in the first half do not come back to haunt them.
It is unlikely that Massimiliano Allegri's side will be so generous at the Allianz Stadium, so it is hard to shake the feeling that Ten Hag's men might live to regret not taking a lead to Italy.
Ronaldo revels on the big stage…again
A virtual spectator for the opening 45 minutes until the final action of the half, Ronaldo demonstrated exactly why he comes alive for this competition. He is now just two away from reaching 600 career goals - do not bet against him hitting that landmark in Turin next week.
Neres spares Van De Beek's blushes
The Ajax midfielder's glaring miss midway through the first half was ruthlessly punished by Ronaldo. The 21-year-old will have breathed a huge sigh of relief when Neres found the back of the net, though, ensuring it is a little less costly than it could have been.
Key Opta facts
- Ajax are now winless in their last 10 matches with Juventus (D5 L5), the joint-longest winless record of one side against another in all European competition, along with Benfica v Bayern Munich (also 10).
- Following a run of 24 wins in 28 knockout games at home in the European Cup/Champions League (D3 L1), Ajax are now winless in their last seven such matches (D4 L3), last tasting victory against Borussia Dortmund in the quarter-finals in 1995-96.
- Juventus have progressed to the next round from six of the previous seven European Cup/Champions League ties in which they have drawn the first leg away from home; though their one elimination did come in their most recent such tie (v Man Utd in 1998-99 semi-final).
- Thanks to his opening goal, Juventus striker Cristiano Ronaldo is now the joint-top goalscorer in the Champions League at the Johan Cruijff Arena with six goals (level with Zlatan Ibrahimovic).
- Only Dusan Tadic (nine) has had a direct hand in more Ajax goals in the Champions League this season than David Neres (four – two goals, two assists).