Gagne's sixth score of the season gave the Kings a 4-0 lead midway through the decisive second period.
After Colin Fraser gave Los Angeles an early 1-0 lead, Alex Martinez, Dustin Brown and Gagne each connected in the middle frame, chasing Wild goalie Josh Harding. Matt Greene scored on replacement Niklas Backstrom before the period was over.
Los Angeles goalkeeper Jonathan Quick turned aside all 14 shots in the first two frames, then allowed a pair of goals in the third, finishing with 24 saves as the Kings won for the second time in three games.
Harding stopped 17-of-21 shots before being lifted and Backstrom made 14 saves.