John McGeever, from Edinburgh, ran on to the Hampden pitch and was involved in an altercation with a Rangers fan after his team won the game 3-2.
He admitted charges under the Offensive Behaviour at Football Act.
McGeever, 44, was given a two-year banning order in 2013 after being part of a football-related brawl in Glasgow.
A Hibernian fan has been fined £2,000 and given a four-year football banning order over his role in the disorder at the end of May's Scottish Cup Final.