Chris Basham's first-half header had put the Seasiders in front at Bloomfield Road but a penalty from Paul Konchesky and an absolute stunner from Andy King - the first goals Blackpool have conceded at home this season - put the Foxes in front.
Yet just when it looked like Leicester had done enough to claim victory, Kaspar Schmeichel felled Gary MacKenzie in the penalty area and Ince kept his cool to fire home from the spot.
From Blackpool's point of view a share of the spoils was a relief after Tuesday's shock defeat to strugglers Millwall had ended their unbeaten start to the season.
"We had a mad five minutes. You can't give Leicester those sorts of chances to get back in the game," Thompson said.
"It was a rash tackle for the penalty and a wonder strike and it changed the game.
"It was a bit gung-ho at the end of the game. We had lads throwing long balls into the box and we used that to our advantage and got a bit of luck at the end with Tom putting the penalty away.
"We dug in, showed our reserves of fitness and spirit and got ourselves a good point against a good Leicester team.
"They had a spell where they penned us in our half and we needed an outlet to give us a breather. You see Leicester - they've got quality in all departments. You have to keep compact and hit them on the break."