The Swedes dominated Russia but only won 3-2 at the Peaks Ice Arena in Provo, Utah
The defeat means that Russia will have to beat or draw with Canada on Thursday to have any chance of qualifying for the medal round.
Canada opened their account with a resounding 7-0 win over Kazakstan at the E Center.
Despite the difference in the scorelines, the matches mirrored each other in that one side was dominant in each game.
Sweden had 44 shots on the Russian goal and were looking comfortable having taken a three-goal lead.
However, the Russians, who were defensively weak, fought back to lose by the odd goal in five.
Sweden's Ann-Louise Edstrand opened the scoring with a power play goal in the first period .
Lotta Almblad and Kristina Bergstrand stretched the lead with two more goals.
Ekaterina Pashkevitch and Larisa Mishina scored for Russia who mustered only 14 shots on target.
Canada forced Kazakstan's Natalya Trunova into 59 saves en route to scoring seven.
Hayley Wickenheiser was the star of the show with two goals and an assist.
Wickenheiser, the youngest player on Canada's 1998 Olympic team and a softball player at the Sydney Olympics, gave her side the perfect start.
After just 2:33 she opened the scoring and from that moment on, the Canadians never looked back.
"We started a little slowly, but by the third period we picked it up," Wickenheiser said.
"Having one Olympics under our belts we're pretty relaxed and we know what we have to do to be successful," she added.
Danielle Goyette and Cherie Piper each had a goal and an assist and Kim St Pierre stopped 11 shots for the top seeds.