Stone scored on a power play at 6:36 of the first period for a 1-0 lead, and Reilly Smith made it 2-0 at 8:20.
"I think it was a wide-open game," Smith said. "There were chances both ways. I don't think it was a typical game for either team, but it seemed like they capitalized on their chances and we didn't. There were a lot of opportunities tonight, but when you play that back-and-forth game, you leave it up to chance."
Boston responded with four unanswered goals.
Pastrnak cut the lead to 2-1 at 11:21, and Marchand tied it 2-2 on a power play at 18:58.
"I actually think we were playing better than they were," Marchand said about the first period. "They just capitalized on their two opportunities. We just kept playing the same way. We're a resilient team. We've shown that plenty of times."
It was the first power-play goal allowed by Vegas in 12 attempts this season.
Marchand gave the Bruins a 3-2 lead 33 seconds into the second period, and Torey Krug made it 4-2 at 2:27.
"They're a great team," Krug said. "We knew what they were going to bring. This game had the potential to go a lot of different directions. Obviously, being down early, being able to come back, winning a close game at the end, those are just some experiences that we'll put in our pocket and use for another day."
Pacioretty scored a power-play goal at 14:42 of the third period for the 4-3 final.
"We feel like we gift-wrapped them their goals," Pacioretty said. "Definitely didn't make it hard on them. After that, we put our foot on the gas, we were just a little too late."