Police dogs and horses were used by officers who lined the streets to try and separate the riots taking place before the friendly match, to mark 20 years since the stadium first opened.
However the match was overshadowed by some of the clashes that took place round the city.
Footage posted on social media showed a flare and other objects being thrown towards Fletcher's News and Booze before fighting broke out on the street.
Officers were called to the off-licence in Hendon at about 1.40pm.
Robinson, the EDL founder, was there wearing a Glasgow Rangers shirt - the arch rivals of Celtic.
One bespectacled Celtic fan was seen bleeding from his head after the running clash.
Following the incident Robinson claimed Celtic fans "armed with flares, bricks and missiles...attacked woman and children in a shop."
In retaliation, a woman wielding a large weapon started swinging wildly at the Celtic fans.
A brawl then broke out between both sets of supporters and they battled back-and-forth on the street.
After a few minor scraps, a Celtic fan was attacked by a man hurling a large weapon. He was repeatedly hit and left bleeding on the floor.
The North East Ambulance Service said he is in a "serious" but "not life threatening" condition.
Northumbria Police issued a warning to fans after the violence broke out.
A spokesman said: "At approximately 1.40pm today, police received reports of an incident at Fletcher's Off Licence in Hendon.
"Police and paramedics attended the scene after damage was caused to the off licence and allegations of assault were reported.
"A man has been taken to hospital with a head injury.
"Police inquiries are on-going to determine the circumstances around the incident."
Elsewhere Celtic supporters drinking in bars near the Stadium of Light were ambushed by a coach full of hooligans.
One witness said: "All the bars around the Stadium of Light were full of Celtic fans singing and having a nice time.
"At about two o'clock a white coach pulled up and off got a lot of soccer thugs, they did not have any identifiable colours of football teams.
"They were singing anti IRA chants and God save the Queen.
"The police got between them. They had to back in all of the thugs to keep them away from the Celtic fans."
A spokesperson for Northumbria Police said: "At approximately 1.50pm police received reports of bottles being thrown outside of the Deaf Centre, North Bridge Street in Sunderland.
"The incident involved both Sunderland and Celtic football fans.
"Police arrived on scene and dispersed the growing crowd."
In total, 21 arrests were made by police.
Prior to the match Robinson had joked about being "banged out" by Hoops fans and randed their supporters "muppets".
The pre-season match was organised to mark 20 years since the opening of Sunderland's Stadium of Light and 50 years since Celtic won the European Cup.
Assistant Chief Constable Helen McMillan said: "Unfortunately we did have some incidents of disorder in and around Sunderland between Sunderland and Celtic fans and while police dealt with them quickly, it is a shame these type of incidents happen at all."
Sunderland were beaten by Celtic 5-0.
