A towering Andy Carroll header midway through the opening period gave England a 1-0 lead over Sweden at half-time in Friday's crucial Group D encounter in Kiev.
England manager Roy Hodgson started Carroll alongside Danny Welbeck and the former justified his manager's faith in him as he leapt high to head Steven Gerrard's cross past keeper Andreas Isaksson.
Having drawn with France in their opener, England needed to win to join the French, 2-0 winners over co-hosts Ukraine earlier in the day, on four points at the top of the group.
Sweden, who have never lost to England in seven previous competitive meetings, were meanwhile facing elimination having already lost to the Ukrainians.
English forward Andy Carroll celebrates with teammates after scoring during the Euro 2012 championships football match Sweden vs England on June 15, 2012 at the Olympic Stadium in Kiev. AFP PHOTO / GENYA SAVILOV