Crawford then sealed the Blackhawks' victory by stopping Tyler Kennedy in the Penguins' last shot.
Patrick Sharp and Bryan Bickell had given Chicago a 2-1 lead, which the Blackhawks held until late in the third period when Brett Sterling got the equalizer for Pittsburgh with less than 4 minutes remaining in regulation.
Crawford stopped three power play attempts for the defending NHL champs, who secured two key standings points as they seek to join the Western Conference playoffs.
Matt Cooke scored and Fleury made 29 saves for the short-handed Penguins, who dropped their fifth game in seven contests while playing without their injured top three goal-scorers.
Swim Week Miami Beach 2014 [PHOTOS]