Rabbi Yehoshua of Sachnin explains that God did not remember or hear the prayers of Yisrael until the time when the supernal minister of Egypt fell from power, as signified by the title verse.
Egypt represents our negative and wicked character traits, and Egypt's minister or King is the root seed of our evil. When we offer up our negative traits by admitting them to ourselves during prayer and meditation and to others during moments of conflict, our prayers then ascend to the Upper World. The act of acknowledgment is the key that unlocks the gates of heaven so that all our prayers will be answered.
As we recall our most vile traits in this moment, and peruse the text of the Zohar, we eradicate the root level of all evil in ourselves, and in this world. All our prayers for peace, endless joy, and eternal life are henceforth answered.