The Kings trailed 2-0 early in the second period of game two in Chicago but struck five times in the final stanza – with Carter scoring three – to triumph by four goals.
Carter became the 12th player in NHL history to score three goals in the final period of a play-off match.
The Canadian centre scored in the second, 15th and 17th minutes of the third term, while Jake Muzzin and Tyler Toffoli struck between Carter’s first two goals, as the visitors bounced back from their 3-1 loss in game one on Sunday.
The Kings and the Blackhawks will now head to LA for games three and four on Saturday and Monday respectively.
At the United Center on Wednesday, Chicago opened the scoring late in the first period thanks to a power-play goal from Nick Leddy.
Ben Smith doubled the hosts’ lead just 1:40 into the second period but with less than two minutes to the second break, Justin Williams struck for LA to make it 2-1.
Carter equalised for the Kings 1:37 into the third period when he deflected Drew Doughty’s slap shot into the net on a power play.
Muzzin scored on another power play less than three minutes later, before Toffoli struck in the ninth minute.
Carter made it 4-2 on a counter-attack and then completed the second play-off hat-trick of his career with a late empty-net goal.
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