Footage taken in Pollokshields, in the south side of the city, showed fireworks being set off by a group in the middle of the street.
The Unison union said residents had seen large groups of young men causing disorder until 02:00, firing "industrial-sized" fireworks at people, buildings and cars, and setting fire to public property.
Ch Supt Lynn Ratcliff, divisional commander for Greater Glasgow, said groups of young people involved in the disorder had been "motivated to cause the maximum amount of fear and alarm".
She added: “This put not only local residents at risk, but meant police officers, fire service personnel and ambulance crews were in danger of being injured, as they responded to protect communities."
No one was injured in incidents in Glasgow and Edinburgh, police confirmed.
A 25-year-old man was arrested and a "significant quantity" of fireworks seized after a search of a van in Drumchapel.
The force said the fireworks were being sold to the general public, including to under-age children.
Meanwhile, in Peterhead at about 21:20, a man was hit by a van driven by individuals who, moments before, had set off a pyrotechnic in a skate park in Aalesund Road.
The 33-year-old was treated by paramedics at the scene but did not need further medical attention.
Two men, aged 62 and 57, have been arrested in connection with the incident.