Kevin Mirallas and Romelu Lukaku struck to sink Leicester and hand Everton their first away win since September.
The pair scored breakaway second-half goals to send the Toffees seventh in the Premier League following a 2-0 victory at the King Power Stadium, which increases the champions' relegation worries.
It was only Everton's third triumph from their last 13 Premier League games but Ronald Koeman's side ground out all three points in a low-quality game.
The last time Leicester hosted the Toffees, in May, they lifted the Premier League trophy afterwards, but this time they are three points above the relegation zone.