awards one point to a team

How can I create a system that awards one point to a team when the opposing team is eliminated? When I swap the teams in the score manager, nothing works anymore and no point is awarded.
For example, I set the Team 1 score manager to give a point when the Team 2 player counter reaches 0, but it does not work. However, if I set the Team 1 score manager to give a point when the Team 1 player counter reaches 0, it works, but it gives the point to Team 1, which is not what I want.