Visiting manager Jon Dahl Tomasson fielded a strong starting XI, with Alexander Isak and Anthony Elanga leading the line and Robin Olsen between the posts.
The Aston Villa goalkeeper could do little about the Luxembourg goal midway through the first half - a deep corner from Danel Sinani was met at the back post by Seid Korac, who headed the ball through Olsen's legs.
Despite the firepower up front, Sweden created little throughout the 90 minutes, registering just two shots on target to the home side's seven.
It could have got worse in the second half for the side ranked 65 places higher than their opponents when Alessio Curci rounded Olsen, only for Isak Hien to make a goal-saving tackle before he could tap it into an empty net.
Vincent Thill also went close late on as Luxembourg pushed for a second.
But one goal turned out to be enough for the home side, who registered a first win over Sweden in seven attempts.
It is an embarassing start to the calendar year for Tomasson and his side, who beat Luxembourg 8-0 in their previous meeting in 2017.
Sweden must pick themselves up ahead of a home friendly with Northern Ireland in Solna on Tuesday.