Dunedin Area Commander, Inspector Dave Campbell said police attended a few relatively minor incidents at the stadium during the Argentina-England clash.
The five arrests involved two for intoxication, one each for disorderly behaviour and trespass, and a streaker was charged with pitch invasion.
The 23-year-old student faces a maximum penalty of a $5000 fine or three months' imprisonment when he appears in the Dunedin District Court tomorrow.
St John treated 13 people at the game for minor medical matters, he said.
"It's pleasing to see that people enjoyed the occasion of the first major international to be held in the city's new stadium," Insp Campbell said.
Traffic flowed well and there appeared to be no significant issues with congestion around the stadium.
A fixed-wing plane employed to monitor congestion points in the city was "valuable" and information from it and those on the ground was "useful in monitoring crowd dispersal".
He apologised to the "few members of the public" who complained about the noise of the plane late in the evening.
English fans Danielle Harbour and Laurie Smith, of Manchester, were savouring their team's win as they walked towards the Octagon.
The atmosphere inside the covered stadium was unrivalled, Ms Harbour said.
"It was fantastic," Mr Smith said. "We were seated way up high out the back, but you could still see everything on the pitch. It all felt so close."
The Octagon had filled up quickly as spectators made their way to the central city, after exiting the stadium.
Inner-city bars filled quickly with patrons and queues formed.
Liquor bans were in place across much of the north and central city, Insp Campbell said.
Senior Sergeant Craig Brown said a further 13 arrests were made after the game, up until 7am yesterday, for a range of offences including disorderly behaviour, offensive behaviour, and trespassing.
"By all accounts, everyone behaved pretty well," he said.
• Police in Invercargill were pleased with crowds at the Scotland v Romania match.
Southland Area Commander Inspector Lane Todd said about 14,000 people attended the game and just two people were warned for intoxication before leaving the ground of their own accord.
St John treated three people for minor medical matters.
