Max Pacioretty scored twice in the first for the Golden Knights (23-15-6), who have won the first three of their season-high seven-game homestand.
"It was a roller coaster. You don't want to put yourself in those situations, but it seemed like we faced every situation tonight, whether it's power play, penalty kill," Pacioretty said. "Overall, it's a good team win. We relied on everyone. Sometimes that makes winning extra special."
WATCH: [All Flyers vs. Golden Knights highlights]
Philadelphia got the 6-on-3, with goalie Carter Hart pulled for the extra attacker, when Deryk Engelland was penalized for cross-checking Jakub Voracek at 18:31 after Reilly Smith was called for delay of game for playing the puck over the glass at 17:14.
Vegas allowed one shot on goal in the final 1:29. Defenseman Brayden McNabb made a diving block on a Shayne Gostisbehere shot with 1:20 left and poke-checked a pass away from Gostisbehere with 1:09 remaining.
"It's busy, just trying to find the pucks through guys and through legs," said Golden Knights goalie Marc-Andre Fleury, who made 34 saves. "Other guys did a great job, [McNabb] made a nice save, a two-pad stack, and got his stick on another puck to clear the puck out of the zone. It's great, a good battle at the end to keep that win."