A scrambled 90th-minute header from Henrik Larsson earned Sweden a share of the spoils but it was not enough to stop England from finishing top of Group B even if their 38-year winless streak against the Scandinavians continued.
The result ensured England will face Ecuador in Stuttgart on Sunday while Sweden's match against Germany will take place on Saturday in Munich.
Substitute Steven Gerrard appeared to have headed England's winner five minutes from time after Sweden's Marcus Allbäck had cancelled out Joe Cole's stunning first-half strike from long range.
But Larsson steered home a long throw on 90 minutes to earn Sweden a precious point and guarantee their place in the last 16.
Despite producing some of their best football of the tournament for much of the game, England greeted the final whistle with relief after surviving a Swedish onslaught for much of the second half.
Sweden hit the woodwork and twice had shots cleared off the line as England suddenly looked horribly vulnerable from set-pieces.
England's draw came at a cost however, with Owen stretchered off in agony in only the first minute with what looked like a serious injury after the Newcastle striker collapsed to the ground in pain.
Earlier, the return of Wayne Rooney in attack and the introduction of Owen Hargreaves in midfield paid off handsomely for Eriksson, giving England a much more balanced look from the outset.
Rooney's physical presence and darting runs were a constant menace, and the Manchester United star had Swedish alarm bells ringing as early as the 10th minute when he raced through to a Joe Cole pass only to be marginally off-side.
In the 25th minute a sumptuous pass from David Beckham sent Rooney bearing down on the Swedish goal. The 20-year-old's first touch wrongfooted the Swedish defence but Rooney's subsequent low shot was well saved by Andreas Isaksson.
Isaksson did not have much of a respite however.
On 29 minutes he was forced to tip a wicked inswinging Beckham free-kick over the bar as the England assault continued.
England's positive play got the goal it deserved on 36 minutes with Cole's stunning effort likely to go down as one of the goals of the tournament.
A headed clearance from Teddy Lucic fell to the Chelsea player outside the area, who chested to control and then uncorked a looping right foot volley that flew into the top corner.
Isaksson got a hand to it but there was to be no denying Cole a fabulous strike.
Yet with England seemingly in control of the game, they suddenly found themselves scrambling almost from the start of the second half and Sweden equalised on 51 minutes.
John Terry deflected a Henrik Larsson shot wide and from Tobias Linderoth's ensuing corner, FC Copenhagen striker Allbäck rose unchallenged to glance a header past Paul Robinson.
Allbäck's strike left England shell-shocked and they were lucky not to fall behind only moments later after another set-piece left them in disarray.
A corner from the opposite flank from Lyon's Kim Källström was met with a wicked header from Freddie Ljungberg which Robinson deflected onto the underside of the bar with an instinctive save.
England's vulnerability from set-pieces saw the introduction of Arsenal centre-half Sol Campbell for Rio Ferdinand shortly afterwards but still the Swedish onslaught continued.
But Campbell was caught out of position when Lucic headed back across the face of goal to skipper Olof Mellberg on 60 minutes, who saw his shot shave the top of the cross bar with Robinson beaten.
With England hanging on grimly, Eriksson withdrew Rooney from the fray for Steven Gerrard, the Liverpool captain stiffening the midfield as they switched to 4-5-1 with Crouch the lone striker.
It was Gerrard who came to England's rescue within minutes, clearing a Källström shot off the line after another well-worked Swedish corner.
And Gerrard, who had been rested to avoid picking up a second booking that would keep him out of the second round, looked to have earned the points for England after nodding in Cole's cross.
But Larsson had other ideas.