Rather than continuing to change the universe, G-d brought it into harmony with Himself. The Zohar tells us that the mystery of the Sabbath is Unity. On the Sabbath, G-d created Harmony between Himself and the universe. When man observes the Sabbath, he too partakes of G-d's eternity. He enters into a state of harmony with both G-d and the world.
Man is then in a state of peace with all creation.
This immediately explains why the concept of peace is so important on the Sabbath. This also gives us a deeper insight into how the Sabbath recalls the Exodus. Both symbolize freedom. All week long, man lacks a certain freedom. He is bound to the material world and is a slave to its pressures.