Anderson had turned aside 44-of-45 shots until Neal put in the rebound of a Robert Bortuzzo shot with a hesitation move that faked the Ottawa goaltender to the ice.
Brian Gibbons got the other goal for the Penguins, who notched a third win in four games.
Stephane Da Costa scored for the Senators.
Interpol investigating stolen passports on missing flight
Senate Democrats to pull all-nighter on climate change