Carter logged a "natural" hat trick, netting three straight goals starting 4:47 into the second period, with the Kings up 1-0 on first-period goal by Dwight king. Carter scored 16 minutes later on a 5-on-3 power play, getting credit for a goal initially given to Anze Kopitar.
Carter capped the performance with 7 minutes left in the final period, scoring on another two-man advantage as the Kings swept two Western Conference finals games in Phoenix and improved to 9-0 on the road in the post-season.
Carter collected the Kings' first playoff hat trick since Wayne Gretzky accomplished the feat in 1993.
Quick turned aside all 24 shots he faced for Los Angeles, which will try to open a commanding 3-0 lead when the series switches to the Staples Center Thursday.
Mike Smith made 36 stops for the Coyotes.