Sweden knew they could not qualify for the quarter finals but they could knock out France by picking up a result in Kiev.
France brought Hatem Ben Arfa into the team to pose his attacking threat, while the Swedes handed starts to Ola Toivonen and Emir Bajrami.
A tame opening period showed no sign of abating as the French sat deep and did not look to have a consistent creative spark.
The deadlock was broken on 54 minutes and it was a sublime piece of individual skill by Zlatan Ibrahimovic.
Kim Kallstrom won the ball in midfield and spread it wide to the right. Seb Larsson's cross was deep and looping but Ibrahimovic swiveled in mid-air and struck a perfect scissors volley to beat Hugo Lloris.
France continued to disappoint their fans as Sweden seemed more at ease with the ball. A header from Olivier Giroud was their best chance, but flew over the bar under little pressure.
The win was sealed by Sebastian Larsson as the match crept into injury time. A cross bobbled around in the box before the Sunderland midfielder lashed it into the roof of the net.
France still progress to the quarter finals, where they face Spain, but their confidence will have taken a dent after a deserved loss.
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