Los Angeles have now won seven consecutive post-season games and are two wins short of reaching their first Stanley Cup finals since 1993.
The Kings have never won a Cup title.
"We really want it right now," Los Angeles forward Dustin Penner told reporters. "It's fear that stops you from letting games get away. We use that fear to motivate us."
The final appeared a distant dream for the Kings who now have earned the unfamiliar tag of the favourites after blowing away West top seeds Vancouver and St. Louis in the opening playoff rounds.
Continuing the good work, Jeff Carter came alive with a hat-trick and Jonathan Quick delivered a 24-save shutout to bring Los Angeles closer to the ultimate series.
Dwight King notched a first-period score for the visitors, his third of the series, and Carter then took over with a pair of goals in the second and one final one in the third.
Carter became the first Kings player to get a playoff hat-trick since Wayne Gretzky in 1993.
Goaltender Mike Smith made 36 saves to display the form that has carried the Coyotes to this point but Phoenix was overmatched at home for the second straight game.
"We got outcompeted again, out-battled," Smith said. "In the first period we played a little better and competed a little harder, but it's not enough."
Los Angeles host the third game on Thursday.