Nigel Pearson's side had to come from behind twice before Huddersfield's resistance was broken by the Foxes who conjured up a second-half performance full of power and invention.
Huddersfield should have taken an early lead when Gary Roberts headed a Danny Cadamarteri cross wide from close range.
But Town had their lead on five minutes when David Martin failed to collect a Roberts corner and after the City defence failed to clear, Phil Jevons pounced to hook home the ball from seven yards.
City levelled on 11 minutes when Bruno Berner's angled drive cannoned into the net off Michael Morrison from six yards.
Tom Cleverley was then a fraction away from getting on the end of Matt Fryatt's low cross before Keigan Parker shot just wide.
Martin was then at full stretch to palm away a 30-yard drive from Michael Collins as Town continued to impress.
City carved out a chance soon after the restart when Andy King rifled just wide after Steven Howard had knocked down a Lloyd Dyer cross.
But it was Huddersfield who recaptured the lead on 51 minutes when Parker took full advantage of a hesitant home defence to lift the ball over Martin from 18 yards.
Leicester equalised for the second time on 59 minutes when Matty Oakley hoisted in a free-kick and Howard nodded on for Berner to drive home at the far post.
After Howard had seen the keeper parry his shot on to a post, City had their noses in front for the first time on 63 minutes when Fryatt notched his 24th goal of the season.
Morrison's close-range shot from a Dyer cross ricocheted off a defender to Fryatt, who chested the ball home from five yards.
The Foxes went on the hunt for a killer fourth goal which duly arrived on 73 minutes, when Howard nodded on an Oakley corner for Jack Hobbs to head home from close range.
Huddersfield's frustration was complete on 88 minutes when they were reduced to ten men.
First Roberts was shown a yellow card for kicking the ball away and then the same player was shown a straight red for using abusive language against the referee.