Sheffield Wednesday's Niclas Alexandersson came off the substitutes' bench to settle a match the Swedes dominated, in the 65th minute. He had been on the pitch for only five minutes, in place of Arsenal's Fredrik Ljungberg, who had to go off after a foul that cost Milen Petkov a red card.
The worst Sweden can do now is find themselves in the play-offs. The world champions, France, would be grateful for any route through from the fearsome Group Four after failing to break down defensive Ukraine in a 0-0 draw in Kiev. With two games to play, Ukraine head the group with 16 points, one more than Russia, Iceland and France.
Russia beat Armenia 2-0, while Iceland won 3-0 against Andorra with a goal each from Brentford's Hermann Hreidarsson and Bolton's Eidur Gudjohnsen.
The French were lifted by the return of their playmaker, Zinedine Zidane, who shot just wide on the stroke of half-time and later had a shot deflected over the bar by Arsenal's Oleh Luzhny.
It was a generally a good day in Europe for north London, although, while most of the Arsenal contingent fared well, their reserve goalkeeper, Alex Manninger, was in the Austrian side beaten 3-1 in Vienna by Spain, who had thrashed them 9-0 in March.
Fernando Hierro scored twice - once for each side. In tackling Michael Hatz in the 50th minute he knocked the ball past his own keeper, but he atoned six minutes later by sweeping a free-kick over the Austrian wall and into Manninger's top right corner. Raul Gonzalez had given Spain the lead in the 25th minute, and Luis Enrique completed the scoring in the 88th.
The Tottenham contingent featured prominently, too. Steffen Iversen set up the only goal for Oyvind Leonhardsen as Norway beat Greece 1-0 to move to the brink of qualifying for the finals for the first time. Allan Nielsen scored the opening goal in Denmark's 2-1 victory over Switzerland that kept the Danes ahead of Wales in Group Five. Jon Dahl Tomasson, once of Newcastle, scored the winner.
Slovenia stayed on course for a first appearance in the finals after consolidating second place in Norway's group with a 2-1 win over Georgia, thanks to another goal by their high-scoring midfielder, Zlatko Zahovic.
The Czech Republic, already sure of winning Scotland's group, underlined their position with a 4-0 victory in Lithuania that aided the Scots' cause.
Luis Figo saved Portugal from embarrassment in Baku with a last-minute equaliser in a 1-1 draw with Azerbaijan in the replayed Group Seven qualifier, which had to be abandoned at half-time on Friday, with the score 0-0, when the floodlights failed. Romania now lead the group after beating Slovakia 5-1 away, with Viorel Moldovan, once of Coventry, scoring twice.Reuse content