By Democrat reporter
Rangers supporters clash with police in Gordon Street, Glasgow, this afternoon.
This power, which police said, is only authorised when absolutely necessary, also allows officers to require the removal of any item the officer believes is being used wholly or partly for the purposes of concealing their identity.
The scenes of disorder came ahead of the match.
Footages on social media shows large groups of fans charging down Argyle Street ahead of kick-off, setting off flares near fearful shoppers.
Police officers can be seen using batons on running fans – some of whom were wearing Santa hats and face coverings.
The force said missiles had been thrown and windows smashed. It said officers had been authorised to use stop and search powers, including removing items being used to conceal identity.
The powers will remain in place until 21:00 in areas including the city centre and parts of the south side, east end and into South Lanarkshire.
Shoppers feared for safety
Many trains had been cancelled ahead of the 15:30 kick-off with ScotRail warning of a driver shortage.
Large groups of fans could be seen walking through the city centre from about 13:00, escorted by police.
However violence soon erupted, with one group charging down Argyle Street towards the Trongate. Shoppers trying to leave can be seen screaming and running back indoors to avoid the rush.
One football fan falls to the group while others run around him shortly before a flare is set off near a shop doorway.
A shopper told BBC News they were forced to take refuge in a nearby shop “for their own safety”.
An officer can then be seen using his baton on a number of fans passing by. On Monday, it was reported that a police officer was injured after being hit by a missile.

The Force have confirmed that one officer was injured during the clash. Police also raced to Gallagher’s bar in Howard Street around 12.30pm after fireworks were lobbed inside the Celtic pub.
Police have confirmed that just two arrests were made during the match. A 41-year-old man was arrested and charged in connection with a drugs offence.
Police also hand-cuffed a 30-year-old man inside the ground for possession of a pyrotechnic. Both men will be reported to the Procurator Fiscal.