England battled to victory despite playing for an hour with 10 men.
Micah Richards (53) grabbed the winner for Stuart Pearce's side at Orjans Vall in Halmstad after they had Michael Mancienne (31) sent off for a professional foul after Lee Cattermole (15) had given them the lead after great work by Gabriel Agbonlahor.
Tim Sparv levelled from the penalty spot before seeing Theo Walcott, his former Southampton team-mate, replaced at the interval in the Arsenal forward's first appearance at a major championship after going to the World Cup with the seniors three years ago but not playing.
Richards' header from a James Milner corner after the break earned England a vital win as their other Group B opponents are Spain and Germany, who are expected to provide sterner tests.
England are next in action on Thursday, when they face the Spanish in Gothenburg.