The goals have been a long time coming for marquee Real Madrid signing Schroder, who had failed to score in her first 11 caps. She was given the ideal opportunity to get off the mark midway through the first half when Loreta Rogaciova fouled Anna Anvegard inside the box, and the teenager coolly dispatched the penalty.
That was the only goal until the 58th minute, when Schroder had her second after combining with former Hacken teammate Anvegard, and only five minutes later she had herself an international hat-trick after being played in by Matila Vinberg.
The 3-0 lead was the signal for Sweden head coach Tony Gustavsson to make changes, and 10 minutes later two of them worked in tandem for goal number four, as Monica Jusu Bah teed up Stina Blackstenius.
Nathalie Bjorn started her first game for Sweden after a long injury lay off, but was withdrawn at half-time. Her replacement, Amanda Ilestedt, completed the 5-0 rout eight minutes from time after good work from another substitute, Filippa Angeldal.
Sweden need only avoid a calamitous home defeat in Solna on 13th October to progress to round two of the play-offs, where they will face Belarus or Italy for a place in Brazil.