Hope Powell’s side finished third in Group C and face a quarter-final against hosts Finland on Thursday.
Faye White gave England the lead from a superb set-piece after 28 minutes, heading home an inch-perfect cross from Karen Carney.
Carney had earned the free-kick in the Swedish half, and when Fara Williams laid the ball to the winger her cross was perfect. White rose highest and guided her header into the far corner.
England endured a heart-in-mouth moment less than a minute later when Victoria Svensson latched on to a loose ball from Lindsay Johnson only to shoot into the grateful arms of Rachel Brown.
Lotta Schelin wasted a great chance to level six minutes before the interval, scuffing her shot wide from Svensson’s nod-down.
But Schelin made amends just moments later when she equalised after being brought down in the box by Katie Chapman.
Svensson picked herself up to strike the spot-kick into the bottom corner.
Alex Scott saved England from going into the break behind when she headed off the line from Schelin’s free-kick.
Kelly Smith almost put Powell’s team ahead in the opening moments of the second period.
Taking down a loose clearance from Swedish keeper Hedvig Lindahl, Smith reacted quickly to fire a looping shot that the keeper tipped superbly over the bar.
Williams met the corner at the near post, only to flash a powerful header inches over.
Smith hit the target with another left-foot volley around the hour and Williams then ran on to Carney’s pass only to see Lindahl smother the ball.
The final stages were a cautious affair as both keepers were well protected.