In The Subtle Knife, the shadows tell Mary Malone she must play the part of the serpent, and later it is clarified she has to play the same part to Lyra that the serpent did to Eve in the garden. Only, I got all the way through The Amber Spyglass and I'm not clear how Dr Malone actually fulfilled that prophesy. Is it just that she got Lyra thinking about romantic love and that caused her to fall in love with Will? Cause if so thats... kinda weak IMHO.
At the end of The Amber Spyglass the abyss or the rupture that the Magisterium's weapon is causing dust to be lost from the world at a great rate. Mary can see this as a "flood" in the sky when she looks through her spyglass.
When Lyra and Will have both come to the world of the mulefa, she talks to Lyra, telling her her story of how she gave up being a nun, of her first relationship, of her loss of faith. She tells a particular anecdote of sharing marzipan with boy when aged 12:
"This boy -- I didn't know him -- he asked me to dance [...] And he took a bit of marzipan and he just gently put it in my mouth -- I remember trying to smile, and blushing, and feeling so foolish -- and I fell in love with him just for that, for the gentle way he touched my lips with the marzipan."
As Mary said that, Lyra felt something strange happen to her body. She felt a stirring at the roots of her hair: she found herself breathing faster. She had never been on a roller-coaster, or anything like one, but is she had she would have recognized the sensations in her breast: they were exciting and frightening at the same time, and she had not the slightest idea why. (AS p.467)
Intentionally or not, Mary is tempting Lyra. Just as the serpent in Gen. 3 doesn't tell Eve to eat the fruit, but just tells her that she can, Mary is teaching Lyra how to express her feelings for Will. This brings Lyra's feelings for Will into focus. Later she shares a fruit with him, placing it in his mouth, showing their love for each other. This acts as a renewed target for the dust to settle upon and heals the rift in the worlds.
The terrible flood of Dust in the sky had stopped flowing. It wasn't still, by any means; Mary scanned the whole sky with the amber lens, seeing a current here, an eddy there, a vortex further off; it was perpetual movement, but it wasn't flowing away any more.
The Dust pouring down from the stars had found a living home again, and these children-no-longer-children, saturated with love, were the cause of it all. (AS p. 496)
The original temptation of Eve had caused a similar settling of Dust. In the bible of Lyra's world, when Adam and Eve ate the fruit, they first saw their dæmons, and this settling of dust caused the change in human behaviour that is really observed about 33000 years ago, when humans began to create "art") (in truth, there is debate about whether there was any change in human behaviour at time - see behavioural modernity)
(page references from the UK Point edition 2001)