Gostisbehere was assessed a two-minute minor for cross-checking. Friedman crashed hard into the boards but got up on his own.
Gostisbehere, 28, has never received supplemental discipline from the league over 380 career outings.
It was a heated affair between the Pennsylvania rivalries. Friedman dropped the gloves with Flyers forward Joel Farabee earlier in the contest, and Penguins captain Sidney Crosby got into a wrestling match with Travis Konecny.
Tuesday's game was the last between the sides this campaign, with the Flyers taking the season series 5-3.
Pittsburgh moved back into the top spot in the East Division with the victory.