The boys, aged 15 and 16, have been arrested on suspicion of violent disorder and are currently in custody.
Police are still gathering video evidence of disorder in the city following reports of criminal damage, arson, assaults and anti-social use of fireworks.
Officers have again appealed for anyone with footage of incidents which happened between 6pm and 11pm in Great Horton Road, Dirkhill Road and Laisteridge Lane on November 5 to contact them.
A separate investigation is continuing into video footage of an attack on a pub in the Manningham area of the city which happened on the same night.
Superintendent Daniel Greenwood, of Bradford District Police, said: "We were clear in the run-up to Bonfire Night that we would fully investigate unacceptable behaviour by those who risked the safety of the wider community by behaving recklessly.
“I hope these arrests will serve as a warning to others that we are taking this seriously and we are taking action.”
Anyone who witnessed any of the above incidents or who may have information or video footage which may assist is asked to contact police in Bradford on 101, quoting reference 13180558484, or use the live chat facility on the West Yorkshire Police website.
Information can also be reported to the independent charity Crimestoppers, anonymously, on 0800 555111.