Van Persie and Robben, missing with an ankle injury and a muscle tear respectively, are big absences for Guus Hiddink's side, who have taken just six points from four games in a tricky qualifying campaign so far.
The third-place Dutch lead Group A rivals Turkey by two points, with Hiddink able to hand in-form Wolfsburg striker Bas Dost his international debut while Sneijder will assume Van Persie's captaincy.
"It will definitely be a tough match but we have every confidence of winning," explained the Galatasaray playmaker.
"We know the importance of the two players [Van Persie and Robben] to the team but we have a very good team and we trust that this will not frustrate us.
"Instead, the two players who will play, I'm sure they will do their duties in the best way. This team will show that we can do this."
Leaders Czech Republic and Iceland will both fancy their chances against Latvia and Kazakhstan, meaning defeat for Turkey or Netherlands would leave them with plenty of work to do to finish in the top two.
Turkey coach Fatih Terim has had to deal with more unwanted speculation over the international future of Omer Toprak in recent days, following his and Hakan Calhanoglu much-publicised off-field disagreement with Gokhan Tore.
Terim went to watch the Bayer Leverkusen pair in the recent UEFA Champions League clash with Atletico Madrid but had no joy convincing them to return to the fold.
"Of course I would love to be on the field in Amsterdam. However, under these conditions, it is not possible to play for Turkey," Toprak told Milliyet.
"I need to trust all my team-mates when I'm on the pitch. If I don't, this does not make sense."
Former Turkey boss Hiddink will once again be keen to make the most of home advantage in Amsterdam, with the Dutch having won both of their home qualifiers so far.
However, Turkey have lost just one of their last five competitive away fixtures - September's 3-0 defeat to Iceland in Reykjavik.
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