Danny Williams then fired just over the back from the edge of the box as Huddersfield asserted their dominance early on.
Vardy was given his first sight of goal just before the break when he connected with Wes Morgan's flick but sent the ball wide as the first half ended goalless.
The second half proved more dynamic as, just a minute in, Depoitre collected Kachunga's pass, muscled out Harry Maguire and drilled a low ball beyond Schmeichel and into the bottom corner.
Huddersfield's lead was short-lived, however, with Leicester winning a penalty in when Chris Lowe was deemed to have brought down Andy King in the area, and Vardy duly fired his spot kick straight down the middle.
In the 61st minute, the home fans thought that they were back ahead, only for Kachunga to be deemed offside when he headed home Mathias Jorgensen's cross, though much to the hosts' chagrin, the 25-year-old was in fact onside.
Both sides continued to weigh in with effort and, in the 90th minute, Demarai Gray went down in the area under Jorgensen's challenge, but the referee waved away the appeals as the match finished all square.