I believe the "working together to save the universe" thing was the episode(s) transitioning between Tom Baker and Peter Davidson (Doctors 4 and 5).

The original Master actor (dead many years now) was my favorite, but the Sam Tyler Master is definitely my second favorite.

For such a strong part of the DW canon, it's hard to realise that the series was almost 10 series old when the character was introduced, back in the Jon Pertwee years (early 1970s).