Roy put the Kings ahead 3-0 at 10:35 of the second period with a wrist shot from the right circle.
Pirri cut the lead to 3-1 at 10:51 with a half slap shot from the slot, and Zykov made it 3-2 at 13:09.
Schuldt got his first point with the primary assist on a long pass that gave Zykov a sharp-angle shot into an open goal.
"I just tried to be in good spots and read the play a little bit. [Zykov] was in a good spot and he put that away," Schuldt said.
Schuldt, who signed an entry-level contract on Wednesday, also blocked one shot while playing 21:03.
"For his first NHL game, and to come into a game like this, every pass he made was on the tape," Gallant said. "He played real good, strong defense, and to make that play to Zykov, definitely a great first game for him."