I've won the first battle for both sides and when I tried to save it doesn't seem to be able to --am I missing something?

When you have completed the mission, either by destroying all enemy units or after all turns have lapsed, a screen will e.g. show "Decisive Victory" with a dialog asking "Save Game" and a thumbs up for "Yes" and a thumbs down for "No".

This screen is bugged by the way - every time you save game on this screen, you will receive prestige points for finishing this scenario.