O'Neill called for his players to go for it pre-match with qualification on the line and they flew out of the blocks against the Dutch outfit, who finish their European campaign with just one point.
Nygren tapped home Kieran Tierney's cross from close range and they doubled their advantage when former Celtic goalkeeper Vasilis Barkas found Nygren with a slack pass.
The Swedish midfielder tried to square it for Daizen Maeda, but it was instead turned in by Viergever as the visitors compounded the initial error.
De Wit was then penalised for handball after a video assistant review (VAR) and Engels dispatched the penalty to put Celtic in total control.
Or so it seemed.
Schmeichel was unmoved as De Wit's shot found the bottom corner and although he made an excellent save to tip Niklas Vesterlund's header round the post, he was unable to keep out Blake's shot down to his left and Celtic's comfortable lead was suddenly nervy.
However, Trusty climbed highest to nod in a fourth and Celtic managed the remainder of the game to make sure their European campaign continues for two more matches at least.