Elswhere, Toronto goalie Ben Scrivens recorded his first career shutout as the Maple Leafs beat Ottawa, John Tavares had a hat trick as the New York Islanders cruised past New Jersey, and Montreal notched a third straight win by downing Philadelphia.
Anaheim goaltender Viktor Fasth was strong in the shootout, allowing only one of three Nashville shooters to score. He improved to 8-0-0 this season, with four of those victories coming in shootouts.
Toronto's Scrivens stopped 34 shots as the Maple Leafs beat the Ottawa Senators 3-0.
Scrivens was making his second straight start since incumbent James Reimer injured a knee on Monday. The 26-year-old Scrivens has been solid as Reimer's replacement, stopping 96 of the 100 shots he has faced.
New York's Tavares scored three times and set up another as the Islanders trounced the New Jersey Devils 5-1.
The Devils' lone goal was Marek Zidlicky's power play slap shot 8:47 into the third.
David Desharnais, Tomas Plekanec and Rene Bourque also scored for the Canadiens, who outshot the tired-looking Flyers 29-19. Gallagher left four minutes into the third period after being hit into the boards.
Daniel Briere scored for Philadelphia.