Tottenham went ahead through Sanchez who scored his first goal for the London club by meeting Eriksen’s whipped cross with a diving header in the 33rd minute.
However, Leicester City’s players complained he was in an offside position.
Leicester City missed the chance to equalize on the hour mark when substitute Jamie Vardy’s penalty kick — his first touch after coming on — was pushed away by Hugo Lloris.
The kick was awarded after Jan Vertonghen was adjudged to have fouled James Maddison in the box.
Tottenham doubled their lead three minutes later as Eriksen collected the ball on the edge of the penalty area and unleashed a fierce shot past goalkeeper Kasper Schmeichel.
Vardy made up for his earlier miss by tapping in from close range to cut the hosts’ lead 14 minutes from the final whistle.
That was after a well-worked move allowed Ricardo Pereira to drill in a cross from the right.
After a sustained period of Leicester pressure, Son settled nerves of the home supporters by slotting in Tottenham’s third goal with a solo run from the halfway line.