That brought up Malkin, who slid a backhander along the ice between the pads of Anderson, handing the Penguins their third win in five games to start the season.
Neal netted the Pens' only regulation goal and Fleury turned aside 31-of-32 shots.
Colin Greening scored in the second period for the Senators, who dropped their second straight after opening the season with three consecutive victories.
Anderson made 33 saves for Ottawa.
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