Antonio Conte's side have recently lost momentum in the race to qualify for Europe's top club competition, taking just one point from their previous two matches with no shots on target.
But Harry Kane eased their nerves when her powered home a header from Son's corner midway through the first half and the South Korean doubled the lead on the hour mark after a pass from substitute Dejan Kulusevski.
Son scored a third in the 79th minute to kill the game, curling an unstoppable effort into the top corner before a late consolation for Kelechi Iheanacho for a Leicester side with players rested for the return leg of their Europa Conference League semi-final with Roma.
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