Victor Piturca's men knew a win was required to guarantee their berth in the last eight while the new-look Dutch were fully aware they needed to impress Van Basten.
As a consequence, the opening moments of the match provided few champagne moments.
However, there was goalmouth action, albeit of the half-chance variety.
Romania's top marksman Adrian Mutu came close on two occasions after creating the openings himself.
His first effort resulted from a clever twist and turn on the left-edge of the six-yard area that was deflected wide by the boot of Wilfred Bouma.
Mutu's second effort was more spectacular - a shot from 25 yards that flew two feet wide of Stekelenburg's right-hand upright.
They should have hit the target just before the break when Paul Codrea fired over from 12 yards following great work by full-back Razvan Rat down the left.
The Dutch went even closer. Demy de Zeeuw threaded the ball to Huntelaar who in turn flicked the ball to Arjen Robben.
Netherlands squad has 'clicked' - Robben
However, the Real Madrid star was perhaps a little too nonchalant, poking his shot a yard past Bogdan Lobont's right-hand post.
By this point it appeared that coach Piturca knew Italy had taken the lead against France and that his team required nothing less than a win.
If the 11 on the pitch did not know the scoreline in Zurich during the first half then they were surely aware of it by the restart.
But instead of throwing caution to the wind the Romanians seemed more cautious and anxious - for that, they paid the price.
The men in white were given a warning by Van Persie whose turn and shot from eight yards was brilliantly saved low by Lobont.
But within 10 minutes the Dutch punished their opponents when Afellay's low ball from the right was calmly converted by Ajax forward Huntelaar.
Foward Daniel Niculae was brought on for Marius Niculae in the hope he would reinvigorate the dispirited Romanians - but there was to be no Turkey-style comeback.
On the other hand, the Dutch looked more comfortable as the game wore on and Van Persie wrapped things up with the vicious strike into the roof of Lobont's net from six yards.
Netherlands: Stekelenburg, Boulahrouz (Melchiot 58), Heitinga, Bouma, De Cler, De Zeeuw, Engelaar, Afellay, Van Persie, Robben (Kuyt 62), Huntelaar (Vennegoor of Hesselink 82). Subs Not Used: Van der Sar, Timmer, Ooijer, Mathijsen,Van Bronckhorst, van Nistelrooy, Sneijder, De Jong, Van der Vaart.
Goals: Huntelaar 54, Van Persie 87.
Romania: Lobont, Contra, Tamas, Ghionea, Rat, Cocis, Codrea (Dica 72), Chivu, Nicolita (Petre 82), Marius Niculae (Daniel Niculae 59), Mutu. Subs Not Used: Popa, Stancioiu, Marica, Sapunaru, Moti, Cristea, Radu.
Ref: Massimo Busacca (Switzerland).
BBC Sport Player Rater man of the match: Netherlands' Robin van Persie 7.94 (on 90 minutes).
Please note that you can still give the players marks out of 10 on BBC Sport's Player Rater after the match has finished.
The Netherlands became only the seventh team to win all three group matches at a European Championship. The five at previous tournaments all made it to at least the semi-finals. Croatia also won all their Euro 2008 group matches.
This 2-0 win gave the Dutch nine goals in the group phase equalling the record set by France in 1984.
Klaas-Jan Huntelaar became the seventh Dutch player to score at Euro 2008 which equals the record for most different goalscorers from a team in the tournament history. Five of the six previous teams with at least six different goalscorers at the European Championship reached the final.
Huntelaar's opener for Holland made him only the eighth Dutch player - Beb Bakhuys did it twice - ever to score in at least five successive internationals and the first since 1974.
The Netherlands have used 22 of their 23 man squad in their three group phase matches. Only third choice goalkeeper Henk Timmer has not been used. Croatia are the only other team to have used 22 players so far at Euro 2008.
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