Both sides had chances in the opening minutes. First Craig Bryson shot wide for the home side from outside the box, before Leicester's Chris Wood placed an effort straight at Lee Grant from distance.
Chris Martin, who scored both goals in Derby's 2-1 win away at Brighton last week, had a good chance after 18 minutes, but his shot flashed over from just outside the box.
However, Leicester then had a great chance to take the lead. Vardy broke clear of the Rams defence but was denied by Grant, who stood tall.
Grant was again in the action just moments later, saving a close-range effort from David Nugent.
However, the Foxes' pressure soon paid off when Vardy forced the ball in, although Grant got the final touch.