Harding was holding back the tears during the national anthem as she reached her century of appearances.
It took Wales until just before the half-hour mark to break the deadlock, a low strike from Green setting the visitors on their way.
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Sophie Ingle then hit the crossbar before Harding toasted her landmark cap, doubling the lead with a close-range finish from Ceri Holland’s cross.
Fishlock wrapped up the points with a well-taken third, opening up her body and scoring from 12 yards to leave Wales with the prospect of qualifying for their first World Cup.
Gemma Grainger’s side cantered to victory in Nur-Sultan as Kayleigh Green opened the scoring before Harding struck and Jess Fishlock sealed the win after the break.