Andy Carroll, making his first competitive start for his nation, had given England the halftime lead with a powerful header in the 23d minute, but Sweden fought back through an unlikely source in Olof Mellberg. The defender had a shot pushed into the net by Glen Johnson for an own goal in the 49th minute, then scored on his own with a header in the 59th.
In the earlier game, Ukraine's players were first drenched by a thunderstorm, then swamped by France's clever passing in Donetsk.
The French ended a six-year drought for a win at a major tournament by beating the cohosts, 2-0, in a match delayed for nearly an hour because of a huge, soaking thunderstorm.
When crackles of lightning lit up the sky, referee Bjoern Kuipers made a quick decision in the fifth minute that the players' safety and the flooded field made it impossible to continue. The match restarted 56 minutes later.
Jeremy Menez and Yohan Cabaye scored early in the second half to help France to its first win in a major match since the semifinals of the 2006 World Cup.
"I hope the next win won't take another six years, because I will be long fired by then," said France coach Laurent Blanc.
Racism concerns continue. Racism remained an issue at Euro 2012 as UEFA received reports that Croatia fans threw a banana toward the field and racially abused Italy striker Mario Balotelli on Thursday.
An antidiscrimination group appointed by UEFA to work at Euro 2012 said Friday it had clear accounts from two monitors that about 300 people in Croatia's end of the Municipal Stadium in Poznan, Poland, directed monkey chants at Balotelli, who is of Ghanaian descent. UEFA is also investigating claims by a Spanish fans' group that some Spain followers made monkey chants at Balotelli during a Group C match last Sunday in Gdansk, Poland.
The federation will also receive details of far-right flags and nationalist symbols displayed by some Croatia followers, officials say.
Croatia faces further charges because the kickoff was delayed by firework smoke after it equalized in the 1-1 draw against Italy.
UEFA has fined the Croatian soccer association $31,500 for its fans "setting off and throwing of fireworks and missiles, and a pitch invasion by a supporter" at Sunday's match against Ireland.
The federation also fined the German soccer association $12,550 because fans threw grapefruit-sized paper missiles at Portugal players during a match on Saturday.
UEFA rules make national associations responsible for their fans' behavior inside stadiums.
Fans take a stand. In Kiev, Ukraine, fans from around the world played soccer together to promote tolerance and combat racism at Euro 2102.
Dozens of fans wearing T-shirts emblazoned with the words "Football Unites" played five-minute matches in the fan zone set up on the city's main street while hundreds of spectators cheered and applauded.
Bradley's Egypt beaten. Former U.S. coach Bob Bradley saw his new team's 2012 unbeaten run come to an end in a shocker, as 10-man Central African Republic beat Egypt, 3-2, in an African Cup qualifier in Alexandria. Egypt has not been defeated in 13 games this year.
It was just Egypt's second international game at home since a riot at a league game in Port Said in February left 74 people dead. The game was played in an empty stadium because of ongoing security worries, given recent political upheaval in the country.
Swansea names Laudrup. The English Premier League club Swansea named Denmark's Michael Laudrup as manager, replacing Brendan Rodgers, who joined Liverpool earlier this month.