The Lionesses began the evening sitting second in League A Group 3, three points better off than Sweden and two behind leaders France, who travelled to basement side the Republic of Ireland.
As a result, Sarina Wiegman's side just needed to avoid defeat to ensure a place at next year's tournament via direct qualification, as finishing third or fourth would have only sufficed for the playoffs.
The Euro 2022 champions did their bit at the Gamla Ullevi, despite coming under the cosh in the second half, although a surprise result in the other group game meant that England missed a golden opportunity to go through as group winners.
Indeed, France suffered a shock 3-1 loss to an Ireland side who had only scored once in their first five Euros qualifiers, but England's stalemate meant that the Blues finished one point clear of Wiegman's side with 12 compared to the Lionesses' 11.
Hannah Hampton makes awkward, but crucial late save
After their unconvincing 2-1 beating of Ireland in their penultimate game, England boss Wiegman stuck with Hannah Hampton in goal over established number one Mary Earps, and the Chelsea shot-stopper earned her keep in the dying embers.
With 83 minutes on the board, England failed to close down Filippa Angeldahl and the Swede responded by pulling the trigger from 30 yards, unleashing a fierce drive which had Hampton scrambling.
The 23-year-old was well-positioned and had the strike covered, but she awkwardly flapped at the ball and palmed Angeldahl's strike right back into the danger area, before Lucy Bronze saved her bacon with a punt upfield, picking up a knock for her troubles.
Leah Williamson fortunate not to concede spot kick
Before Hampton's lucky escape, Leah Williamson was also thanking her lucky stars inside the England penalty area, as she went lunging in on Rosa Kafaji after the Swedish substitute was played through by Johanna Rytting Kaneryd.
However, rather than hitting the deck - as she would have been entitled to do - Kafaji perhaps tried to be too honest, staying on her feet and trying to keep the attack going, only to see her cross deflected out by Millie Bright.
There were no fierce appeals from those in yellow, but Wiegman's side could certainly count themselves fortunate that Kafaji tried to do the right thing, which so often goes unrewarded in such situations.
More to follow.