Leicester, who face Atletico Madrid on Wednesday in the first leg of their Champions League quarter-final, made five changes ahead of their trip to Spain and the defeat ended the run of five straight wins since Craig Shakespeare replaced Claudio Ranieri as manager.
For Everton, it was a fine bounce back from their derby defeat to Liverpool and the disappointment of conceding an injury-time equaliser to Manchester United in their 1-1 draw on Tuesday.
Ronald Koeman's team grabbed the lead after 30 seconds when Kevin Mirallas broke through from midfield and appeared to be brought down but the referee, wisely, played advantage and the ball fell to Tom Davies who shot home.
Leicester struck back three minutes later though with a trademark counter-attack, Demarai Gray bursting deep into home territory before he slipped the ball to Islam Slimani and the Algerian coolly side-footed past Joel Robles.
Robles was beaten again in the 10th minute when he misjudged a curling free kick from the left from Marc Albrighton as the champions took a 2-1 lead.
Everton looked the sharper in midfield with Mirallas particularly lively and it was no surprise when they got back on level terms in the 23rd minute, Ross Barkley whipping in a superb cross from the right which Lukaku met with a perfect glancing header –- the Belgian scoring for the eighth straight home game.
Four minutes before the end of an intense first half, Everton grabbed the lead. Barkley should have scored when one-on-one with Leicester keeper Kasper Schmeichel but the Dane managed to palm it wide for a corner and from the resulting kick Phil Jagielka rose at the back post to power in a header.
Lukaku struck again, with his 23rd league goal of the season, in the 57th minute, firing home at the back post after Leicester failed to clear a corner.
Robles made amends for his error with a superb diving save, three minutes from the end, to keep out a fine header from Leicester sub Leonardo Ulloa.
Koeman said he was pleased with his team's performance particularly the displays of Lukaku and Barkley, who had come in for some criticism after the Merseyside derby.
"We played some fantastic football in the first 45 minutes, really good team performance today. We had great movement between the lines.
"Lukaku and Barkley didn't need to respond (but) they showed today they are fantastic football players. Two players on a high level but the whole team played well."
(Reporting by Simon Evans in Liverpool; Editing by Clare Fallon)
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