After the break, the game came to life, as Mahrez brilliantly volleyed home in the 53rd minute, before Slimani deftly added a second seven minutes later for his first league goal of the season.
Huddersfield had just one shot on target all match as they struggled to get going, while Leicester gave a run out to new signing Adrien Silva after he was given clearance to play. Marc Albrighton netted a late third to seal a victory that sees Leicester stay eighth, while Huddersfield remain 11th despite their first defeat in five.
"We lost our focus and concentration, we were 1-0 down and had to open up, left some spaces, which they used," Huddersfield boss David Wagner said.
Leicester striker Jamie Vardy missed out through injury, as Slimani started just his second Premier League game of the season. The Algeria international had little impact in the opening 45 minutes, with a much-changed Huddersfield rarely troubled, defensively.
"After the end of the first half, perhaps it was not enough - we lacked quality," Leicester manager Claude Puel said. "We came back in the second half with the same spirit to play football on the floor and with quality."
Leicester did really up the tempo in the second half, and they were soon in front after some Mahrez magic.
Albrighton looped a cross into the middle, Mahrez watched the ball onto his left foot, before expertly guiding a volley into the net from a tight angle.
Soon Leicester led by two, with the Algerian again at the heart of the action. An inch-perfect pass from Mahrez allowed compatriot Slimani to race clear before coolly lofting the ball over Huddersfield goalkeeper Jonas Lossl to score.
Huddersfield didn't show any sign of even coming close to getting themselves back in the game, giving Leicester chance to blood Silva for a relaxed debut.
Albrighton won't score many easier goals than his stoppage time strike to make it three, as he slotted into an empty net at the back post to ensure Leicester began 2018 in positive fashion.
(Reporting by Peter Hall; Editing by Christian Radnedge)
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