While it's true that your spacecraft would have to 'counter that gravity' to escape, that's from the frame of reference of the planet. From the frame of reference of whatever distant object you want your craft to 'accelerate' towards, your craft will appear to have gained momentum. If it were a zero sum game- there would be no "gravitational slingshot" effect (aka gravity assist maneuver).

The way your spacecraft 'steals' kinetic energy from the planet it orbits is by using the "gravity" of the planet. The two objects never come into physical contact with one another, the mass of the ship and the mass of the planet effect each others path through space-time- although very slightly. That is to say they seem to 'pull' on each other- what we call gravity.

The Earth and the Moon likewise 'steal' energy from each other through 'tidal' interactions. This causes the Earth to rotate more slowly and the moon to recede from our planet- this is all due to 'gravity'.

Black holes also have kinetic energy that you can 'steal', to boost yourself toward a third celestial body just like planets do.