Even though England and Germany have advanced to the next round, authorities have expressed concerns over soccer hooligans from both countries.
Immediately after that match, Cologne police were forced to separate several German fans from a group of 100 to 200 England fans.
The two groups had started to sing taunts at each other. Officers moved through the street to divide the two sides, a strategy used in Nuremberg and Frankfurt to quell potential problems before they escalated.
There were no reports of trouble in Berlin immediately following the Germany-Ecuador match.
In Cologne, 13 England fans were arrested early Tuesday morning after skirmishing with officers or fighting with each other, police said. Sixteen officers were injured, none seriously.
And more fans are coming. At Cologne-Bonn Airport, more than 100 fan-filled charter flights from both England and Sweden were scheduled to land Tuesday.
"It's going to be the most challenging day of the tournament" to date, said Stephen Thomas, a British constable working with German and Swedish police in Cologne.
Cologne police superintendent Stefan Schwarz agreed, but said authorities were prepared.
For the most part, a party atmosphere prevailed, with England and Sweden fans drinking and snapping pictures with one another.
It was a contrast to the early morning incident in a downtown square, which began after an Englishman scaled a statue to plant a flag on its outstretched arm, but lost his balance and fell several feet to the street. He was not seriously injured.
As German police moved to provide first aid, Thomas said, members of the surrounding crowd threw glass bottles. The resulting brief melee, during which police in riot gear used pepper spray to control some in the crowd, resulted in the 13 arrests -- six fans for clashing with police and seven for fighting.
The fans would be released later Tuesday and issued orders to leave the city, police said.
Following the scuffle, German police arrested eight Sweden supporters, Swedish police spokesman Lennart Petersson said. The Swedes were not involved in any altercation -- they were arrested because they have been involved in previous fights at sporting events and authorities didn't want trouble Tuesday, he said.
The melee in Cologne was an exception at this World Cup. Since the tournament started June 9, hundreds of thousands of fans have watched games and partied; only an approximate 2,700 nationwide have been arrested or detained by police related to the World Cup, most for minor crimes, Thomas said.
Meanwhile Tuesday, in the central city of Hanover police were checking buses and other vehicles carrying fans from Poland, which beat Costa Rica 2-1. Two known German hooligans were arrested at car parks on the city's outskirts, police spokeswoman Katharina Zwerg said.