Schelin scored Sweden's opening goal on 22 minutes, heading in a superb free-kick taken by Magdalena Ericsson.
Blackstenius made it 2-0 in the 51st minute as she picked up a poor goal kick by Russian keeper Tatiana Shcherbak, beat two defenders and fired a shot that Anna Kozhnikova only managed to deflect into the net off the post.
"Three points, two goals, that's good," said Sweden coach Pia Sundhage. "I'm happpy about the result and parts of the performance, especially in the first half."
Russia could have secured a quarter-final berth if they had won, following their surprising 2-1 win over Italy in the Group B opener.
But they never got close as Sweden put them under heavy pressure from the start with Kosovare Asllani's long-range shot smacking the crossbar on 10 minutes.
It took Russia half an hour to threaten up front, but Elena Danilova missed from long range.
At the other end, Schelin shot narrowly wide across goal and Linda Sembrant headed wide from a corner just before half-time.
Sweden continued to dominate in the second half but squandered their chances, with Sembrant heading against the post five minutes from the end.
"Sweden were very strong when it comes to set pieces, there were a lot of them and this was something that didn't allow us to play well," said Russian coach Elena Fomina.
In the other Group B game, defending champions Germany edged Italy 2-1.