Alessia Russo put the Lionesses ahead in the first half, nodding home Lauren James' inviting cross. However, Sweden struck back later on through Fridolina Rolfo, who snuck in behind Lucy Bronze to head home.
The match - played in front of 63,248 fans at the national stadium - was a far cry from England's dominant 4-0 victory over Sweden in the Euro 2022 semi-final, with the visitors posing a constant threat on the counter-attack in a much tighter affair.
Uncharacteristically, Sarina Wiegman's team struggled to control possession, allowing Sweden several opportunities. Arsenal's Stina Blackstenius had a golden chance to put the visitors ahead but blazed her shot wide from close range.
England themselves created very little throughout the game, with only late efforts from Lauren Hemp and Beth Mead proving to be the only noteworthy moments for the home side.
The Lionesses face a tough qualification group, with only the top two teams progressing automatically to the Euros in Switzerland next summer.
England's next test comes on Tuesday when they travel to Dublin to take on the Republic of Ireland. They will also face France, currently ranked third in the world, during their qualifying campaign.
Elsewhere, Scotland kicked off their qualifying campaign with a drab goalless draw against Serbia, but a Jess Fishlock inspired Wales got off to a flyer with a 4-0 win over Croatia.
