Northern Eire were heading within the reliable route for one of the most finest ends in their historical previous when Josh Magennis headed them in front within the 75th minute in Rotterdam, and in addition they were serene heading within the reliable route for a necessary point after Memphis Depay's strike left it at 1-1 going into stoppage time.
But instead they ended the night third in Group C, level on points with the Dutch and the Germans, who have both played a game less and who will both face Northern Ireland next month.
Magennis' goal came from two such mistakes, the first a frightful slice from Juventus' defender Matthijs de Ligt before the experienced Daley Blind failed to deal with the consequences.
But Luuk de Jong then poked Holland in front and Depay rubbed salt in the wounds with his second deep into time added on.
"How we reacted was great", said Dutch captain Virgil van Dijk.
Thompson will now be hoping to make his second start for his country when Northern Ireland take on Czech Republic in a friendly on Monday.
The Dutch ratcheted up the pressure in the second half when Donny van de Beek came on, with centre back Jonny Evans clearing his lines in the 71st minute as Wijnaldum looked to steer the ball home from a hard angle.
Ronald Koeman had described Magennis's goal as like an "axe in the neck" for Holland but was proud of the way they picked themselves up.
Earlier on Thursday, bottom team Estonia picked up their first point with a goalless draw away in Minsk against Belarus.
Last year's World Cup finalists top Group E with 13 points from six matches and will secure their berth with a game to spare if they beat Ryan Giggs' side in Cardiff tomorrow.