The group of mostly young men appeared to overwhelm the security officials working the game, and players waited patiently as the visitors were rounded up and removed from the field.
Francesco Totti scored the only goal on a cross from Alessandro Florenzi from the right side in the 58th minute.
AS Roma nearly made it 2-0 about a minute later, but Adem Ljajic had a close miss. Real Madrid's Isco shot just right of the goal in the 60th minute.
AS Roma played tight defence from there to keep its championship hopes alive. AS Roma can advance to the championship game with a win over Inter and a loss by Manchester United on Saturday.