Jamie Vardy opened the scoring after just 11 minutes, smashing the ball in from the right-hand side of the box after a dominant opening spell by the home side.
The Foxes doubled their lead just before the break when David Nugent delivered a corner into the box that missed his teammates, but was turned into the box by Anthony Gerrard, while the visitors had few chances in the first half.
Huddersfield made a strong start to the second period as James Vaughan and Sean Scannell both had chances to reduce Leicester's lead early on, but it was an own goal from Paul Konchesky that got Huddersfield back into the match in the 68th minute.
The visitors continued to press to get back on level terms, but they had to finish the match with 10 men after Vaughan was dismissed for a bad foul on Liam Moore late on.
Huddersfield threw everything at the Leicester goal in the last five minutes, forcing two corners, but they were hampered by Vaughan's absence, and were unable to find a second goal.