Will Cuylle scored, and Igor Shesterkin made 30 saves for the Rangers (14-12-1), who are 2-8-0 in their past 10 games.
“I don’t know what to say anymore,” Rangers forward Artemi Panarin said. “But we had tons of chances again, we should score, but we don’t. Chances don’t win the games, we know that.
“We have to score, hopefully again. I feel like I say that 100 times already, hopefully next game.”
The Rangers outshot the Blackhawks 14-9 in the first period, but then were outshot 23-16 over the final two periods.
“I believe the second and third period, the effort dipped from where it was in in the first period and the execution was worse,” Rangers coach Peter Laviolette said.
“The execution was off all night. Could be fatigue, could be mental, could be anything, regardless, it’s unacceptable. We have to be better than that, but we are not going to win hockey games if we can’t execute.”
Soderblom was starting in place of Petr Mrazek, who went on injured reserve Sunday with a groin injury sustained in the loss to the Jets.
It was his second win of the season for the Swedish-born goalie (2-6-1) and his first since Nov. 9 against the Anaheim Ducks.
“That was so much fun, the most fun I’ve had in a while,” Soderblom said. “It was fun to play here, kind of a childhood dream, watching (former Rangers goalie Henrik) Lundquvist growing up, so it was a cool feeling stepping on that ice and playing as well as we did.”