Rookie Anze Kopitar had a short-handed goal and Alexander Frolov scored for the Kings. Sean Burke stopped 23 of 24 shots in his Kings debut before getting injured. He departed with 16:40 left in the third period after making a couple of rapid-fire saves on rebound attempts by Phoenix captain Shane Doan while on his knees.
Yutaka Fukufuji relieved Burke and surrendered the tying goal, a wrist shot from the top of the right circle by Nagy that bounced off the rookie's glove with 6:02 left in regulation. Roche got the game-winner on a shot from above the right circle that caromed off defenceman Mattias Norstrom's skate with 1:39 to play.
Burke, a 17-year veteran who turns 40 years old on Jan. 19, was claimed off waivers from Tampa Bay on Thursday because of injuries to Dan Cloutier and Mathieu Garon - and the failure of Fukufuji and fellow rookie Barry Brust to provide the Kings with NHL-calibre goaltending over the previous four games.
This is the eighth different NHL franchise for Burke, who spent parts of five seasons with Phoenix.
A standing room-only crowd of 18,346 Staples Center cheered their lungs out during a pre-game ceremony in which the Kings retired Luc Robitaille's No. 20 jersey.