Ings scored his 12th Championship goal of the season to earn Burnley a point in the top-of-the-table battle.
A 14th-minute penalty from David Nugent gave Leicester the lead but Ings punished some poor defending by the Foxes to make it 1-1 in the 47th minute.
Both sides could have snatched a winner in a close game but the 1-1 final scoreline was a fair reflection of the match.
Leicester made three changes from the side beaten at Brighton a week ago. Fit-again Ritchie De Laet returned at right-back after missing nine games while Liam Moore and Anthony Knockaert were also recalled to the starting line up.
Burnley, who deposed City at the top of the table with a 1-0 win against Barnsley, had one change with Dean Marney replacing Brian Stock.
De Laet showed just how much he had been missed with a barnstorming run down the right in the third minute but from his cross Lloyd Dyer saw his shot blocked.
The Foxes had come out of the blocks in rapid style and Burnley were pegged back in their own half for long spells.
Another sweeping move ended with Danny Drinkwater firing in a shot that was scrambled away and minutes later Tom Heaton just managed to beat away a fierce volley from Knockaert.
It had been all Leicester and it was no great surprise when then took a deserved lead in the 14th minute.
Under pressure Jason Shackell gave the ball away to Nugent with a poor pass out of defence. Nugent found Drinkwater who in turn fed Jamie Vardy with a neat ball into the penalty area.
But the City striker went down under the combined challenge of Shackell and Ben Mee and referee Andy D'Urso immediately pointed to the spot.
Nugent made no mistake to net his 11th goal of the season - seven of them from the penalty spot.
City's pace up front continued to trouble Burnley and Dyer sped past three defenders only to see his cross cleared. But Burnley weathered the storm and Ings came close to an equaliser in the 25th minute with a glancing header that hit the far post.
It was the Foxes however who continued to dominate and they should have increased their lead shortly before half-time. Paul Konchesky set Nugent free on the left but from his low cross Vardy dragged a shot just wide of the post.
Then Moore fired over the bar as City ended the half well on top.
But they were rocked in the second minute of the second half when some poor defending gifted Burnley an equaliser.
Kieran Trippier put over a low cross from the right which City failed to clear and Ings made them pay scoring with ease from inside the six-yard box.
Five minutes later Burnley should have scored again. This time a poor clearance fell to Sam Vokes but Kasper Schmeichel rescued his side with a fine save low down to his left.
It was now Burnley who were looking the more dangerous side and Konchesky was fortunate not to be penalised when he sent Michael Kightly toppling in the penalty area.
But against the run of play the Foxes came close to snatching the lead in the 75th minute. Dyer crossed from the left and Gary Taylor-Fletcher, on for Nugent, put in a shot that was deflected just wide.
In time added on the Foxes went close again when Knockaert's shot was palmed away by Heaton and Duff cleared off the line.