Andrew McDonald, Claude Giroux and Radko Gudas also scored for the Flyers, who won for the fourth straight time and moved within one point of the second-place Pittsburgh Penguins in the Metropolitan Division.
Neuvirth improved to 7-7-2 this season with his second victory in 24 hours after making NHL history in a 4-3 shootout win at Arizona on Saturday night. Neuvirth became the first goalie to enter a game during a shootout and earn a win, replacing starter Brian Elliott, who sustained a lower body injury. The Philadelphia sub facing five shots Saturday before Nolan Patrick netted the game-winner in the seventh round.
Brayden McNabb scored the lone goal Sunday for Western Conference-leading Vegas, which fell to 19-4-2 at home and lost back-to-back games at T-Mobile Arena for the first time in the team's young history. The Golden Knights, who were opening a season-high, seven-game homestand, fell 2-1 to the visiting New York Islanders on Jan. 25 before departing on a six-game road trip.
Marc-Andre Fleury finished with just 14 saves for Vegas, which also lost for the third time in five games despite outshooting the Flyers 39-18.
Vegas, which fell to 22-3-0 when scoring first, opened the scoring with McNabb's fourth goal of the season. The wrist shot from the top of the left circle whistled past Neuvirth's glove at the 11:22 mark of the first period.
Philadelphia tied it less than seven minutes later when Couturier, cutting toward the net, jammed in a crossing pass from Travis Konecny between Fleury's pads for his 28th goal of the season.
The Flyers, despite getting outshot 15-7 in the second period, took a 3-1 lead with two goals in the final three minutes before the second intermission. The first came when McDonald, positioned to the left of the net, redirected a shot from a whirling Couturier in the slot. Giroux followed with his 18th goal of the season with 5.8 seconds left in the period, one-handing a loose puck that Couturier had carried in and shoved in front of the net.
Vegas pulled Fleury with 2:40 to go, and Gudas sealed it with his first goal of the season 16 seconds later, rifling a shot from his own blue line into the empty net.
--Field Level Media