Los Angeles took a 1-0 lead at 7:34 of the first period when Ryan scored on a wrist shot from the left circle. It was his first goal with the Kings after signing a one-year contract July 1 as a free agent.
Ryan went 65 games without an NHL goal; he hadn't scored since Feb. 25, 2018, for the San Jose Sharks against the Minnesota Wild.
Dustin Brown had the assist, his fourth point (two goals, two assists) in four games.
Prokhorkin made it 2-0 at 12:12, putting the rebound of a shot by Trevor Lewis over Brossoit's blocker from close range. Prokhorkin had been scratched for the previous two games to allow Lewis to get back into the lineup after missing eight games because of a lower-body injury.
Prokhorkin also won 5 of 7 face-offs (71 percent) in a game where the Kings managed 45 percent (25 of 56).
"He's a talented player," Kings coach Todd McLellan said. "There's a bit of a rotation that's happening there, but he stayed ready, took advantage of his opportunity. You know, when some of our other centers were getting drilled early in the circle, he was actually winning a fair number of draws, so that was a real positive as well."