Germany coach Joachim Low named a side without a striker but goals from wingers Serge Gnabry and Leroy Sane, symbols of their new generation, established a 2-0 half-time lead.
Memphis Depay recorded a goal and an assist as Netherlands came from behind after the interval to seemingly claim a point at the Johan Cruijff ArenA on Sunday.
Germany, though, earned revenge for last year's 3-0 Nations League defeat against Ronald Koeman's side, when wide man Schulz got forward to finish brilliantly with his weaker right foot.
A Gnabry effort called Jasper Cillessen into early action before a perfectly timed Frenkie de Jong challenge halted the run of Joshua Kimmich, but Germany's high-tempo start produced the opening goal in the 15th minute.
Toni Kroos sent Schulz scampering down the left and, after neatly controlling the cross, Sane capitalised on De Ligt's costly slip to slam home an excellent finish on the volley.
Manuel Neuer made two key saves in quick succession from Ryan Babel and Germany then extended their lead in stunning fashion in the 34th minute.
Antonio Rudiger's long ball sent Gnabry one on one with Virgil van Dijk, the Bayern Munich winger cutting in off the left, feinting to create space and crashing home his fifth Germany goal.
Netherlands got one back within three minutes of the restart, though, De Ligt rising highest to glance home a header from a superbly delivered left-wing Depay cross.
And Depay equalised in the 64th minute, indecision in the Germany box allowing Georginio Wijnaldum to tee up the Lyon attacker for his seventh goal in eight internationals.
Both sides seemed to have settled for a point in the closing stages but Germany snatched all three at the death.
Substitutes Ilkay Gundogan and Marco Reus combined to free Schulz and he picked out the bottom corner with an unerring strike to spark a new dawn for German football.
What does it mean? Revenge for Germany
Low's decision to drop World Cup winners Thomas Muller, Mats Hummels and Jerome Boateng raised eyebrows and the way his vibrant and unpredictable side approached the first half indicated putting faith in a younger generation could pay off.
Tactical tweaks from Koeman at the half-time interval put Germany on the back foot and Netherlands looked set to cause more misery for the 2014 World Cup champions after last year's Nations League thumping.
But it was Germany who were left to celebrate as Schulz, earning his sixth cap, won the points.
Goals galore for Gnabry
Few players can make Van Dijk look slow and clumsy, but that is just what Gnabry did in beating the world's most expensive defender before scoring Germany's sensational second goal.
The 23-year-old has now scored six times in his last nine appearances for club and country and is becoming increasingly influential for Bayern and Germany.
Babel wasteful for Oranje
Germany dominated the first half but Netherlands still created two good chances for Babel.
On both occasions he placed his effort too close to Germany captain Neuer and it was no surprise to see Babel make way for Steven Bergwijn at the half-time interval.
Netherlands face England in the Nations League semi-finals on June 6. Germany are away to Belarus and at home to Estonia in a double-header of qualifiers in the same month.