Ronaldo – fit to feature after recovering from a thigh injury suffered on international duty with Portugal last month – put the visitor 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 host 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 its task next week a little easier.