The Wolves giant showed why Premier League clubs are tracking his progress with a hat-trick of fine fingertip saves from long range.
Sneijder twice tested the young keeper, once with a quick free-kick, while Rafael van der Vaart forced him into a full-stretch save.
Robben gave a reminder of his attacking craft and quality as the winger gave young full-back Chris Gunter a torrid time down the Dutch right-flank.
He waltzed past the Tottenham defender to tee-up up club-mate Ruud van Nistelrooy but the former Manchester United striker was expertly thwarted by Craig Morgan's last-ditch challenge.
Toshack praised his young side's attitude
And it was no surprise that Robben was the man to ignite the 50,000 capacity De Kuip crowd as he made a mockery of the Wales defence on 35 minutes.
The ex-Chelsea man capitalised on Carl Robinson's misplaced header to sprint 40 yards past Gunter and slide the ball past the helpless Hennessey.
Robben's ninth international goal inspired an air of authority about Marco van Basten's men in their final game before the European Championships.
Dutch keeper Edwin van der Saar was not tested until two minutes before the break but Freddy Eastwood's shot from edge of the area was easily gathered in.
The Netherlands were in cruise control as Wales grafted hard just to remain in touch.
Robben again tore through the visiting defence but his angle after rounding Hennessey was too acute and he failed to convert.
Sneijder, though, did find the net in the 55th minute as the 23-year-old superstar whipped in a sublime 25-yard free-kick.
He unintentionally almost doubled his goal account as another long-ranger was deflected on to the bar by Swansea defender Ashley Williams.
Bellamy demands his side improve
Young Ched Evans set substitute Craig Bellamy free for a rare goal-scoring chance for Wales but the striker's rasping shot was beat out by Van der Sar.
His opposite number Hennessey had to perform heroics once again as his 6ft 4ins frame somehow denied substitute Jan Vennegoor of Hesselink from point blank range.
The Dutch will not be permitted to remain in cruise control in Euro 2008's 'Group of Death.'
Wales' youngsters, on the other hand, have been given a masterclass by the total football architects of what it is like at the very top.
Netherlands: Van der Sar, Ooijer, Mathijsen (Vennegoor of Hesselink 80), Heitinga (Melchiot 46), Van Bronckhorst (De Cler 46), De Zeeuw (Kuyt 46), Engelaar (De Jong 46), Van der Vaart (Afellay 67), Sneijder, van Nistelrooy, Robben.
Subs Not Used: Timmer, Bouma, Stekelenburg, Huntelaar, Boulahrouz.
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