Sweden shocked the USA 2-1 in the final game of Group C but both teams are into the last eight. Sweden topped the Group after this win with both their goals arriving in the first half.
The Swedes took the lead when midfielder Lisa Dahlkvist scored from the penalty after 15 minutes and doubled their advantage when captain Nilla Fischer's effort deflected into the net off a US player.
The Americans pulled a goal back when veteran forward Abby Wambach netted in the 67th minute but Sweden held out for a famous victory over the two times World Champions in front of over 23,000 spectators in Wolfsburg.
Sweden will now play Australia in Augsburg on Sunday, the same day group runners-up the United States take on Brazil.
"Today was just one of those days," said US striker Abby Wambach.
"You couldn't really argue with the penalty.
"We are just happy to be in the quarter-finals, although we would have loved to have finished top of the group."