Monahan took a pass from TJ Brodie and shot by Jeff Glass' blocker to give Calgary its first win since Jan. 14.
The goal came after Michael Frolik tied the game 3-3 at 9:50 of the third period.
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"When you're out there with guys like Johnny [Gaudreau] and [Brodie] and you find yourself open, you're going to get the puck," said Monahan, who leads the NHL with eight game-winning goals this season. "I think the goalie had my number all night, so I was happy to put one by him."
Matt Stajan and Gaudreau also scored, and Mike Smith made 25 saves for the Flames (26-18-8), who are 1-2-4 in their past seven games.
"It's big," Monahan said. "I think it just comes down to it mentally. You overthink it when you start losing games the way we've been doing. To come back and get the two points tonight, it's obviously important, especially for our mindset here moving forward."
Nick Schmaltz, Vinnie Hinostroza and Anthony Duclair scored, and Glass made 35 saves for the Blackhawks (24-20-8) who have lost two in a row and six of their past eight (2-4-2).
"We've got to keep getting points," Schmaltz said. "We keep talking about it. Everybody is winning every night. It's not going to get any easier from here on out."
Chicago took a 1-0 lead at 7:40 of the first period when Schmaltz one-timed a pass from Patrick Kane over Smith's shoulder. Schmaltz has 14 points (eight goals, six assists) in his past 14 games.