Combat and Movement Points

[Enigma]

Does combat consume a movement point in addition to the movement point it takes to move into a sector.

I am attempting to concentrate my fleet against a slightly faster force. They are going to be jumping through one of my warp points next turn. If I sacrifice a ship at the warp point and force them into combat, that would allow me to move my main fleet onto the warp point and destroy the enemy. This only works if the combat consumes a movement point in addition to the one it takes to move into the Sector. Any help would be appreciated.