David Alaba was pivotal throughout, providing the crosses for both Janko's goals before curling home the third, with Martin Harnik slotting the ball into the net in injury-time to complete the win.
It was nothing more than Austria deserved as they look to make up for a stuttering start in Group C which had seen them take just one point from two games.
The pair shared a 0-0 draw last time out but with both sides shooting from distance in the early stages a repeat did not appear likely.
The visitors were twice grateful to Andrey Sidelnikov, first the goalkeeper parrying Martin Harnik's drilled right-footed shot before collecting Zlatko Junuzovic's subsequent header.
So, it was no surprise when Austria took the lead in the 23rd minute when Janko headed Alaba's right-wing cross into the bottom left of the goal.
Goalbound shots by Marko Arnautovic were kept out by Sidelnikov and the hosts came even closer when Alaba volleyed a 25-yard shot against the post as Austria laid siege to the Kazakhstan goal.
The second half resumed in the same fashion, Sidelnikov again coming to Kazakhstan's rescue from Alaba, but another Austria goal looked on the cards and it duly arrived in the 64th minute.
Again Alaba was involved, his right-wing cross headed home from six yards by Janko and it was 3-0 just seven minutes later.
This time Alaba was the scorer, curling a left-footed shot into the top left of the goal with Harnik rounding off the rout in injury time.