Malkin set up Chris Kunitz's goal midway through the first period for a 1-0 Penguins lead, and then assisted on second-period tallies by James Neal (his 19th of the season) and Tyler Kennedy. His trio of helpers gave him 24 for the season, fourth-best in the NHL.
Fleury stopped all 19 shots he saw in the first two periods and then hung on during a furious Blackhawks comeback in the final frame, improving to 17-7-2.
Jonathan Toews registered his 19th goal and Viktor Stalberg scored for Chicago in the third period, but the Hawks couldn't find the equalizer.
Ray Emery gave up three goals on 28 shots for Chicago, which had a five-game winning streak snapped.
Celebrity Couples of 2014 [PHOTOS]