Without burning fuel acceleration happens:-
Just consider some space craft is fired from earth & moving with velocity more than escape velocity of Mars & it is passing through gravity of mars with its fuel tank empty. Then
1) Definitely due to Mars gravity it will first accelerate & attend the velocity much more than escape velocity & near to Mars, it will move in curve path. This spacecraft will again escape from Mars gravity. Now, as it will go away from Mars, its velocity will definitely get reduce to some extent.
2)When spacecraft is approaching the Mars increase in the kinetic energy happens, means work is done. Who is doing the work?
Gravity as force doing the work
or
curve space applying force & doing the work.
3) Ultimately who is loosing the energy co-ordinate system directly in contact is loosing the energy or Mars apply the force & loose the energy when kinetic energy of space craft increases..