Congratulations tend to pass from the loser (or their fans) to the winner (or then fans) and so are a direct opposite of commiserations, which are from a winner to a loser.
to express pleasure to (a person), as on a happy occasion:
They congratulated him on his win.
This is often seen at the end of a game show in the form of:
Commiserations to [losing team], but congratulations to tonight's winners [winning team]!
This also fits if you want to fit this into your situation of two winning fans:
They congratulated each other on another win for their team.
Russian fans congratulate each other in the street after the finish of the Russia-Czech republic soccer match at Euro 2012, in Moscow
(Alamy Photograph Title)