In Mytischi, Peter Podhradsky scored twice to lead Slovakia to a 5-1 win over Germany and a place in the qualifying round, while Switzerland joined Sweden in advancing out of Group A with a 2-1 victory over Italy.
Backstrom was one of eight players to score for the defending world and Olympic champion, which improved to 2-0.
Jorgen Jonsson passed from behind the net to Backstrom, who beat Latvia goaltender Edgars Masalskis before many of Sweden's fans had settled into their seats.
"It felt good to get that early goal," Backstrom said. "Our line didn't play that well in the first game but we're starting to get some good chances and hopefully we can keep it up."
Despite having only two players from the NHL on its roster, Sweden has outscored its first two opponents by a combined 15-3.
Slovakia, the 2002 world champion, scored only once in the opening period when Podhradsky shot a loose puck between Oliver Jonas' pads during a power play.
However, the Slovaks got a boost from new additions Marian Hossa, Marian Gaborik and Pavol Demitra, who were all added to the roster Monday.
Gaborik, recovering from a virus, and Hossa, shaking off jet lag, combined for a spectacular goal.
Gaborik stormed down the boards, leapt over a prone German defenceman and fed Hossa. The Atlanta Thrashers forward then rushed the net, faked Jonas with a quick short pass to the left, which Gaborik banged in to make it 4-1.
In Group A, Ivo Ruthemann scored Switzerland's second power-play goal of the game with 8:03 remaining, tapping in a rebound to give the Swiss their second win in as many games. Ruthemann's goal came 7½ minutes after Luca Ansoldi had tied the game 1-1.