The City defender crossed for Denzel Dumfries to head home in the matchwinner in Amsterdam, after the 1988 Champions had surrendered a two-goal lead.
Second-half strikes from Georginio Wijnaldum and Wout Weghorst had handed Frank de Boer's side the lead on home soil before Ukraine fought back late on with quickfire Andriy Yarmolenko and Roman Yaremchuk efforts.
Just when it looked as though the spoils would be shared, Dumfries rose highest to convert Ake's delivery, tipping the enthralling encounter in the Oranje's favour.
Our two City stars were both involved with Zinchenko completing the full 90 minutes at the heart of midfield, while Ake was introduced from the bench on 64 minutes.
Although entertaining with plenty of goalmouth action, the first half ended goalless - only for the clash to spark into life after the break.
Two goals in six minutes before the hour looked to have given the Netherlands a comfortable advantage but a Yarmolenko wonderstrike and Yaremchuk header levelled the score.
It would be Ake who would be celebrating though when Dumfries converted his cross late on to mark the Netherlands' first Euros encounter since 2012 with a victory.
Elsewhere in Group C, Austria gained the perfect start to their campaign with a 3-1 win over North Macedonia.
Ukraine face North Macedonia on Matchday Two (17 June, 14:00) before the Netherlands and Austria lock horns (20:00).
The final group stage games see Ukraine and Austria, and North Macedonia and the Netherlands meet - both at 20:00 on 21 June.