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First off, I would suggest updating to Magento 2.1.3 first, since this changes some fundamental ways on how products are saved.

Secondly, you need to catch a hook on where the product is saved. An event or a plugin (interceptor) could be used for this.

You could add a plugin before the save method of the product repository:

public function beforeSave(
    \Magento\Catalog\Model\ProductRepository $subject,
    \Magento\Catalog\Api\Data\ProductInterface $product,
    bool $saveOptions
) {
    ...

    return [$product, $saveOptions];
}

Or a plugin for the save()-method on the resource model:

public function beforeSave(
    \Magento\Catalog\Model\ResourceModel\Product $subject,
    \Magento\Framework\Model\AbstractModel $object
) {
    ...

    return [$object];
}

Or catch the event (I believe in 2.1.2 you can still use catalog_product_save_before, but in 2.1.3 the saving of the product is done with the entity manager. I'm not sure if this event still exists in 2.1.3). Haven't had time to test this out yet.

For any of these options I would suggest looking at the Price Modifier (Magento\Catalog\Model\Product\PriceModifierInterface). This has a modifyPrice()-method that allows you to set a new price for a product.

protected $priceModifier;

public function __construct(
    \Magento\Catalog\Model\Product\PriceModifierInterface $priceModifier
) {
    $this->priceModifier = $priceModifier;
}

public function changePrice()
{
    ... get price and product ...

    $this->priceModifier->modifyPrice($price, $product);
}

Haven't had the time to test any of the above yet, but perhaps it helps you find your solution.