Captain Zlatan Ibrahimovic's 24th minute strike and an Erkan Zenkin marker just after half-time was enough to guarantee maximum points for Erik Hamren's side and improved their record to five wins, three draws and two defeats.
But it still left them two points shy of Russia while Austria had already won the group.
Swedish fans cheering after they defeated Moldova. Photo: Fredrik Sandberg/TT
That means 1992 Euro semi-finalists Sweden, who have not missed the knock-out stages since Euro 96 in England, must now negotiate a two-legged play-off against a yet-to-be determined opponent.
Austria, with a record of nine wins and one draw, top the pool on 28 points with Russia on 20 and Sweden on 18.
Zlatan Ibrahimovic scoring against Moldova on Monday. Photo: Fredrik Sandberg/TT
Sweden's only appearance in the final of a major tournament was when they lost the 1958 World Cup final, 5-2 on home soil, against Pele's Brazil, but they did win the gold medal at the 1948 Summer Olympics, when they defeated Yugoslavia 3-1 at Wembley in London.
Their tally of 18 points was just one point shy of Ukraine's accumulation of 19 points, ahead of their home match against Spain, in the battle for the best third-placed team and an automatic berth for France.
Swedish coach Erik Hamren. Photo: Fredrik Sandberg/TT