The Parkhead team’s fans initially took to the pitch to celebrate the 4-2 victory on penalties.
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But scenes turned ugly when Rangers fans joined the fight, with flares thrown and police and stewards forming a barricade between the two sides.
The disorder quickly calmed down and fans returned to the stands.
Green smoke could be seen over the Celtic side of the stadium (PA Media)
It was the first time Celtic supporters were given a full allocation of the Broomloan Stand at Ibrox since it was reduced to less than 1,000 in 2018.
Traditionally, around 7,500 Celtic fans filled the stands at Old Firm derbies.
Since then, away assignments at both Ibrox and Celtic Park have fluctuated between around 750 and zero in a series of tit-for-tat moves.
The Scottish Football Association condemned the fans who jumped onto the pitch and said an investigation would be carried out “immediately”.
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Scotland’s victims and community safety minister Siobhan Brown said the scenes were “unacceptable”.
She said: “Of particular concern is the reckless use of pyrotechnics which could have caused serious injuries.”
Brown highlighted that the Scottish Government had recently consulted on expanding powers to ban football fans from matches and was “considering next steps”.
Currently, Football Banning Orders (FBOs) are only imposed if fans are involved in violence or disorder: they allow authorities to prevent fans from attending matches anywhere in the UK for 10 years.
Both clubs told BBC Sport they would not yet comment officially.
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In a post-match interview, Celtic manager Martin O’Neill said: “You’re asking me a lot of political questions at the moment when I’m in a state of euphoria.
“The fans have been overflowing, great scenes at the end, everywhere. I’m not going to diminish it at all, I’ll think about it and talk to you in due time.”
Meanwhile, Rangers manager Danny Rohl told Premier Sports: “I’m not sure what happened at the end, I was in the tunnel.”