Eppur si muove.
Very little of the Saturn V's mass goes translunar -- about 65 tons of it, around 2% of the launch mass. Most of the launch mass of the rocket is propellant, which is burned and exhausted, and returns to Earth.
The moonward-bound portion leaves Earth traveling at about 10.8 km/s, with a kinetic energy of about 3.5 TJ.
Even the lunar-bound portion of the Saturn-Apollo stack doesn't reach Earth's escape velocity, though it does get close. The moon hasn't escaped Earth's gravity, after all, so the spacecraft doesn't need to in order to get there.