Burnley grabbed a fourth-minute lead when Hamza Choudhury's poor pass back to Wilfred Ndidi was intercepted on the edge of the box by Vydra and the Czech striker blasted past Kasper Schmeichel for his first league goal of the season.
Despite the absence of key creative players James Maddison and Harvey Barnes, Leicester were a threat going forward and got reward for their endeavours with an impressive equaliser in the 34th minute.
Ndidi floated a beautifully weighted ball towards Iheanacho in the area and the Nigeria's timing and technique was perfect as he volleyed past Pope.
The New Zealander, who had scored in his last three games against Leicester, his former club, forced Schmeichel into a superb diving save at the foot of the post with an angled header from a fine Matt Lowton cross.
Burnley midfielder Ashley Westwood struck the post with a drive from outside the box as Sean Dyche's side, still with a nervous eye on the relegation zone, searched for the full points.
"We didn't make a good start but showed the mentality of the players to come back into the game," the Leicester manager said.
"We didn't start the second half well but then I felt as the second half wore on we could go on and win the game and we nearly did."
Dyche was happy his team had shown the energy and defensive discipline for which they are known.
"It is pleasing in the sense of coming off a very tough game against Tottenham. Their keeper was arguably man of the match. I was really pleased with our approach play, it was much, much better," he said.
"Leicester are a good outfit despite having a number of injuries like ourselves. You can't be too greedy and the performance was important, getting back to what we are about."