You’re right. A rocket with enough fuel in it would eventually leave the Earth’s gravitational field, even if the velocity is less than the escape velocity. This is because the rocket’s engine is propelling it constantly with enough thrust to counter the effects of the gravitational pull.
In the other hand, escape velocity is the initial minimum speed threshold required for an object thrown or launched upwards from the surface of the Earth so that the projectile would leave the gravitational field without the need for any propulsion or work. So if you were to launch a rocket at 11.2 km/s, it can theoretically leave the gravitational field of the Earth without any further thrust from the engine. The concept of escape velocity usually applies to projectiles (objects that are not powered).