Steven Gerrard [ Images ] put England back in front with a header from a Cole cross four minutes from time, but Henrik Larsson [ Images ] brought the scores level again after a long throw deceived the defence.
England were rattled by the sight of Owen leaving on a stretcher and struggled to keep possession for the opening 20 minutes against a combative Sweden side, who have not lost to them in 38 years.
Fredrik Ljungberg was a threatening presence while defender Teddy Lucic sent in a superb angled drive from a corner that was charged down by Frank Lampard [ Images ].
Wayne Rooney [ Images ], in his first World Cup start after a substitutes' appearance in last week's 2-0 win over Trinidad & Tobago, helped redress the balance with some nice passes and a shot that ricocheted off Lucic.
It was nothing compared to the subsequent candidate for one of the goals of the tournament.
Cole controlled a headed clearance by Niclas Alexandersson with his chest and struck a long-range shot that keeper Andreas Isaksson could only touch on to the inside of his post as it flew in.
However, the sense of euphoria among England fans and the team's clean sheets at these finals lasted only six minutes after the break.
Tobias Linderoth curled over a corner from the right and Allback's glancing header beat keeper Paul Robinson and Ashley Cole [ Images ] on the line.
Sweden were nearly 2-1 up minutes later when Ljungberg's header was parried on to the underside of the bar by Robinson in a goalmouth melee.
Eriksson replaced Rio Ferdinand [ Images ] with Sol Campbell in central defence but the next chance fell to Sweden when captain Olof Mellberg hit the top of the bar.
Sweden had a nervous England side on the ropes and were clearly looking to deliver the knockout blow, prompting Eriksson to swap Rooney for Gerrard.
Gerrard promptly cleared off the line with his first touch after a Kim Kallstrom effort and then put England ahead in the 85th minute with a firm header from a far post Cole cross.