Sweden took the lead when midfielder Lisa Dahlkvist netted a penalty after 15 minutes and the Swedes extended their lead on 35 minutes when captain Nilla Fischer fired in a free-kick which deflected off a US player.
The Americans pulled a goal back when veteran forward Abby Wambach netted in the 67th minute for the 1991 and 1999 world champions, but it was not enough.
“Today’s win gives us some confidence which is really important, especially looking at our next game against Australia,” said Sweden coach Thomas Dennerby.
With both sides already through to the quarter-finals, the result means Group C winners Sweden now play Australia in Augsburg on Sunday, the same day group runners-up the United States take on Brazil in Dresden in a mouth-watering tie.
After her player-of-the-match performance against the USA, Olympique Lyon striker Lotta Schelin said there was no relief amongst the Swedes at missing out on playing unbeaten Brazil in the last eight.
“I haven’t really thought about it, we are just focused on playing Australia,” she said.
“They can play well too, you can compare them to Brazil, so they are all we are worrying about.”
Sweden’s Nilla Fischer was simply happy to have reached the quarter finals.
“Quarter finals are quarter finals, we’ve reached our goal, and the opponent doesn’t really matter,” she said to newspaper Dagens Nyheter.
Sweden dominated the opening stages as player-of-the-match Lotta Schelin was denied only by a brilliant save from US goalkeeper Hope Solo after just six minutes as the pair went one-on-one with the US defence well beaten.
Soon after Japanese referee Etsuko Fukano pointed straight to the spot and booked US defender Amy Le Peilbet for downing Schelin in the box on 15 minutes.
Sweden’s Lisa Dahlkvist then put her side ahead by drilling home the penalty.
The goal forced the the United States into life and Wambach was only denied by Swedish goalkeeper Hedvig Lindahl’s fine save on 20 minutes in front of a crowd of 23,468.
It was end-to-end stuff in the first half as Schelin’s shot on 30 minutes was only snuffed out by some robust defending from US captain Christine Rampone, while at the other end striker Amy Rodriguez hit the crossbar seconds later.
Sweden went 2-0 up when midfielder Nilla Fischer drilled in a low free-kick which deflected off the luckless Le Peilbet’s thigh and looped past Solo into the US goal on 35 minutes.
Lindahl’s busy evening continued as she denied US midfielder Cari Lloyd’s fierce drive on 42 minutes as it finished 2-0 at the break, with the Americans having had 11 shots on goal in the first-half alone.
After a period of sustained second-half pressure, Wambach opened her Germany 2011 account on 67 minutes when the 31-year-old rose highest from a corner.
The ball went in off her shoulder for her 119th goal on her 161st appearance for the Stars and Stripes, but still counted.
With less than five minutes left, substitute Kelley O’Hara wasted a golden chance to level when she fired wide from all of 10 yards with the goal at her mercy.
And Schelin looked to have wrapped up the game when she slotted her shot home from a tight angle on 90 minutes, but her effort was ruled offside.