The Blackhawks had forced overtime when Marian Hossa forged a 2-2 tie on a power-play goal with 4:19 left in regulation.
But the Flames responded in overtime when Russell's 55-foot shot from the blue line deflected off Chicago's Andrew Shaw, banged off the crossbar and past Crawford for the game-winner.
Reto Berra stopped 42-of-44 shots to earn the victory.
Patrick Kane notched a goal and an assist, and Crawford made 27 saves for the Blackhawks, whose three-game winning streak was snapped.
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