Los Angeles scored on its two power plays in the first period to take a 2-0 lead.
Fiala scored from just above the goal line to make it 1-0 at 10:25. Doughty took a point shot that missed on the short side, but the puck hit the end wall and came out the other side to Fiala.
Kopitar had the primary assist for his 757th in the NHL, tying Marcel Dionne for the most in Kings history.
Gudas then went to the penalty box, and Arthur Kaliyev scored with a wrist shot from just above the right circle to make it 2-0 at 12:26.
"We knew they had a tendency to take some penalties and we wanted to be prepared," Los Angeles coach Todd McLellan said. "That was powerful for our group to get rolling there."
Quinton Byfield deflected Vladislav Gavrikov's shot between Gibson's pads to extend the lead to 3-0 at 1:17 of the second period.
"I was just trying to get to the net," Byfield said. "That's what the coaches say, good things happen when you get there, so I just tried to get there."
Fiala made it 4-0 at 2:56 when he drove to the net and waited out Gibson as he skated through the top of the crease before scoring short side.
Fiala said playing on a line with Moore and Phillip Danault had helped his game.
"We have the same type of vision," he said. "All three guys are really fast going to the net. We cycle the puck, we grind down and also, defensively, we do a good job, so it's been good."