Two Celtic team-mates, Johan Mjallby and Henrik Larsson, scored the goals which gave the Swedes victory. They have nine points from their opening three qualifiers and lead Group Five, two points clear of England (who have played a game more) and three ahead of Poland, whom they meet in Chorzow on Wednesday.
Larsson's neat header set up Mjallby for the first goal 10 minutes before the interval and he added the second three minutes from the end. However, it was an otherwise lacklustre display from the Swedes and they should have put more than two goals past Luxembourg, who have lost all three qualifiers.
Liverpool's Patrik Berger scored the second goal from the penalty spot late in the second half in the Czech Republic's 2-0 win over Lithuania in Teplice. The Czechs, who were watched by the Scotland manager Craig Brown, are now five points clear of the Scots at the top of Group Nine, having won all their qualifiers.
Michal Hornak headed the first goal in the first half for the Euro 96 runners-up. The Czech defender Tomas Repka was booked for the second time in the campaign and will miss Wednesday's qualifier against Scotland at Celtic Park.
Turkey are top of Group Three, Northern Ireland's section, after a 2-0 win over Moldova in Istanbul. Hakan Sukur opened the scoring with a fine header in the 34th minute before a Sergen Yalcin shot sealed the points in the final minute. The Turks were helped by the dismissal of Moldova's midfielder Oleg Shishkin on the hour for a reckless tackle.
The Manchester United striker, Ole Gunnar Solskjaer, kept Norway's qualification quest on course with two goals in the 2-0 Group Two win over Greece in Athens. The Norwegians have dislodged Latvia from the top of the table.
Italy are in charge of Group One after goals from Filippo Inzaghi, in the first minute, and Antonio Conte, in the 70th, secured a 2-1 victory over Denmark in Copenhagen.
The eagerly awaited Group Four encounter between France and Ukraine in Paris ended goalless. Ukraine's Andriy Shevchenko missed the best chance late in the game when, clean through, he sent his shot straight at the French goalkeeper, Fabien Barthez.
The Bristol City defender Vilmos Sebok grabbed a hat-trick in Hungary's 5-0 Group Seven victory over Liechtenstein in Budapest, but the day's top scorer was Spain's Raul Gonzalez, who struck four in Spain's 9-0 thrashing of Austria in Valencia. The Spaniards are still only third in Group Six, though.