Jamie Vardy took his tally to 18 goals for the season with a match-winning brace including a stunning opener from about 25 yards on the hour-mark.
10 minutes before the break, Mahrez again tested Mignolet, this time with a well-struck effort from range which the Belgian was forced to flick over his own bar.
The Foxes finally struck 15 minutes into the second half when Mahrez played a long ball into the path of Vardy who allowed it to bounce once before unleashing an unstoppable volley from range on an angle to send the King Power Stadium faithful into raptures.
The lead was soon doubled in the 71st minute when Okazaki's deflected effort fell perfectly for Vardy who needed no second invitation to slot beyond Mignolet with his left foot to wrap it up for Claudio Ranieri's men who continue to pick up points against the odds.
For Jurgen Klopp's Reds, they suffered a third defeat in their past five outings to fall to 8th on the table.
2015/16 BARCLAYS PREMIER LEAGUE - SEASON SCORES