Aaron Mooy scored the only goal for already relegated Huddersfield on the day he met an American girl who gained inspiration from the midfielder's shaven head during her cancer treatment.
Tielemans curled in the opener from 20 yards in the 24th minute before Vardy latched onto Ricardo Pereira's pass and produced a fine finish three minutes into the second half.
But Maddison sealed the game with a free-kick in the 79th and Vardy then converted in the 84th from the spot after being hauled down by Terence Kongolo.
Leicester climbed to seventh in the league.
Huddersfield's special guest, seven-year-old mascot Bella from Texas, was flown over from Dallas after revealing that Mooy was her unlikely hero during last summer's World Cup after she lost her hair during treatment for brain cancer.