Clayton Keller cut it to 4-3 at 7:48 with a wrist shot from the left circle after a backhand feed from Kessel.
Meier gave the Sharks a 5-3 lead at 14:13 when he swatted the puck out of the air past Scott Wedgewood's blocker.
Moser, a 21-year-old defenseman, scored his second of the game on a power play at 19:37 to make it 5-4.
"I'm just glad that I could help the team," Moser said. "Those pucks, or at least one of them, will be at my apartment. Or maybe I'll ship it home."
Tomas Hertl scored his 15th goal of the season at 1:44 of the third period to give the Sharks a 6-4 lead.
Crouse scored his second goal on a rebound at 7:35 to make it 6-5.
"You give up a two-goal lead once, OK, that happens in the game, but to do that three times, that's just over the top," Boughner said. "I don't think [Reimer] was at his best, but he didn't have a lot of support. On a couple of goals, guys were standing around."