Sweden beat Moldova 2-0 at Friends Arena but they will go into Sunday's draw for the Euro 2016 playoffs following Russia's victory over Montenegro.
Erik Hamren's men went into the final round of Group G fixtures two points behind Russia and relying on a favour from Montenegro, who could not deliver as they fell to a 2-0 defeat in Moscow.
Sweden, who have ultimately paid the price for defeats to Russia and Austria last month, will at least prepare for next month's playoffs on the back of a second straight victory, which came courtesy of goals in either half from Zlatan Ibrahimovic, his 59th in international football, and Erkan Zengin.
It was one-way traffic right from the word go in Stockholm, with John Guidetti scuffing a shot against the post in the fourth minute and Ibrahimovic seeing a weak close-rang effort cleared off the line soon after.
Ibrahimovic did not have to wait too much longer for another sight of goal after springing the offside trap and taking a long ball from Mikael Lustig down on his chest before rounding Ilie Cebanu to slot home.
The Paris Saint-Germain striker had an opportunity to add to his 24th-minute opener but headed wide, while Guidetti shot over as Sweden continued to dominate.
The points were effectively in the bag two minutes into the second half when Cebanu raced out of his penalty area to head the ball away from danger, only to see Zengin drop a 25-yard lob into the far corner.
Moldova's first effort came in the 74th minute as Ion Jardan headed over and they had a last-minute goal ruled out after Igor Armas fouled Sweden goalkeeper Andreas Isaksson.