The Terriers had earlier taken the lead courtesy of Laurent Depoitre but a draw was a fair result after a tight match between two evenly matched sides.
Town started well with Tom Ince finding Depoitre whose powerful header was kept out by Kasper Schmeichel before Danny Simpson was forced to turn Tommy Smith’s dangerous cross away for a corner.
When the Foxes responded, Smith managed to deny Kelechi Iheanacho with a last-ditch tackle but Huddersfield continued to have the upper hand, with Aaron Mooy a constant menace.
The best chance Craig Shakespeare’s side created in the first period came just before the interval when Vardy hooked his shot wide after being set up by Wes Morgan’s long ball.
David Wagner’s team made the perfect start to the second half as Depoitre was too strong for Harry Maguire before firing a left-footed effort past Schmeichel.
However, the visitors grabbed a 50th-minute equaliser when Andy King was adjudged to have been brought down by Chris Lowe, and Vardy beat Jonas Lossl with his penalty.
As play continued to ebb and flow, Huddersfield thought they had regained the lead when Elias Kachunga got the final touch on Mathias Jorgensen's effort, only for the goal to be disallowed for offside.
Both teams had late chances to grab a winner, with Vardy only just failing to latch on to Riyad Mahrez’s excellent cross while Ince flashed a shot inches wide with Schmeichel beaten.