Vilhena, 18, has been in sublime form for Feyenoord so far this season and could make his senior debut only weeks after he was capped at Under-21 level for the first time.
Meanwhile, Sneijder, Stekelenburg and Van der Vaart make their comeback after missing the international friendly against Italy last month.
Ron Vlaar, Bruno Martins Indi and Jeremain Lens missed out on the initial squad, but have now received a call-up, while Jean-Paul Boetius, Mike van der Hoorn, Jetro Willems, Bas Dost and Adam Maher were all cut from the provisional roster.
Tim Krul and Klaas-Jan Huntelaar are among those who miss out due to injury.
The match against Estonia takes place at the Amsterdam ArenA on March 22, before the Oranje host Romania four days later.
|Ron Vlaar||Aston Villa|
|Bruno Martins Indi||Feyenoord|
|Ricardo van Rhijn||Ajax|
|Stefan de Vrij||Feyenoord|
|Jonathan de Guzman||Swansea|
|Rafael van der Vaart||Hamburg|
|Siem de Jong||Ajax|
|Robin van Persie||Manchester United|
|Arjen Robben||Bayern Munich|