Needing Northern Ireland to fail to beat Netherlands in order to secure a place at the finals with victory on Sunday (AEDT), Joachim Low's men initially struggled to hold up their end of the bargain.
Indeed, Germany laboured for 41 minutes until Matthias Ginter belatedly netted and teed up a second-half stroll.
Leon Goretzka swept in the second, Kroos added the third and then a brilliant fourth, while Group C rival Northern Ireland was held, setting celebrations in motion in Monchengladbach.
Germany was quickly on top and Aleksandr Gutor had to be alert to react to a deflected Ginter drive, smartly turning the ball around the post.
But the wayward hosts then toiled and an unmarked Timo Werner miscued a header in the centre of goal with the 20th attempt of the first half.
Manuel Neuer was required to bail out his wasteful colleagues, springing to his left to deny Igor Stasevich before blocking from Denis Laptev on the follow-up.
That scare shocked Germany into action, and Ginter's deft flick from a low Serge Gnabry cross deceived Gutor for the opener.
Ginter had a role to play in the second shortly after the restart, too, dummying Kroos's corner for Goretzka to pick out the bottom-left corner.
Gutor dived low to keep out Werner's latest effort but was helpless as Kroos sent a side-footed shot inside the right-hand post from 20 yards, assisted by Ginter.
There was time for further Neuer heroics, however, as the Bayern Munich star saved Stasevich's penalty after a clumsy foul on Pavel Nekhajchik from Robin Koch.
Kroos would have the final say, controlling on the turn inside the area, dummying into space and sliding in a low finish for number four.