Raanta made two great saves on Patrick Kane, and another dazzling save on Richard Panik midway through the middle frame to keep the game scoreless.
Chicago appeared to break through with 14 minutes to play on a goal by Marian Hossa, but New York challenged the play was offside and won to negate the goal. It was the team's first successful challenge of the season.
Raanta admitted there were nerves entering the game, but those quickly evaporated and he settled down to turn in the first shutout of his season.
"Of course [there were nerves]. First time here in this building, how loud the fans can be and the National Anthem when it's starting," said Raanta, who is now 15-0-3 at United Center. "When you get the first save you pretty much don't think about those anymore, you just focus on the next shot. It was great to come here and play. A little nervous but it was a good thing that it ended like this."