There was no way back for a disappointing Scotland side when Baktiyar Zainutdinov's header made it 3-0 in the 50th minute.
Kazakhstan, 117th in the FIFA rankings, looked dangerous every time they attacked on the slick artificial surface and Scotland managed only two attempts on target on a night to forget for them.
"It was disappointing not to see a great reaction (to going 2-0 down)," Scotland boss Alex McLeish said.
"At halftime we tried to change the system a little to unsettle Kazakhstan. They were first to the second balls and, after a good start, we just didn't get up to speed.
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"Unfortunately, the Kazakhs were a team on fire tonight."
With Belgium expected to cruise the group and Russia also strong, Scotland's hopes of automatic qualification already look forlorn, although they are guaranteed a place in the playoffs after topping their Nations League group.
It was all too easy for the Kakakhs as a simple ball forward split the Scotland defence in the sixth minute and Pertsukh took a touch before driving high past keeper Scott Bain.
Scotland barely had time to compose themselves before their defence again went missing to allow Vorogovskiy to slide home from Islambek Kuat's superb pass.
Kazakhstan failed to win any of their 10 games in the qualifying campaign for the World Cup finals but could celebrate one of their greatest nights when Zinutdinov headed home.
Scotland take on San Marino at the weekend while the buoyant Kazakhs host Russia.
(Reporting by Martyn Herman; Editing by Christian Radnedge)
