Ricardo Pereira’s late header sent Leicester into the FA Cup quarter-finals at the expense of in-form Championship side Birmingham.
The full-back guided Marc Albrighton’s cross past Lee Camp to settle the tie just when it looked as if extra time was inevitable.
James Maddison had earlier gone close to breaking the deadlock when his 25-yard shot hit the crossbar.
The Foxes – who had not scored in the previous four games – fully deserved their first victory in six matches.
Leicester City manager Brendan Rodgers told BBC Sport: “It was always was going to be [a tough game]. Their record unbeaten tells you how well organised and resilient they are.
“I thought it was just a matter of time [before we scored]. In the second half we dominated – lots of quick combos and the goal was coming. It was an excellent display. Some real good moments of play against a team who make it very difficult for you.
“The performance was very good. When you go 1-0 up it becomes a war in the last few minutes. We stood up to it very well.”
Birmingham manager Pep Clotet also spoke to BBC Sport: “We always try. We were not naive. We knew we needed to be organised. We had a solid performance – showed organisation and worked hard. They only had two shots on target.
“That little bit of quality yielded a goal. But afterwards we went higher and tried to get a goal. We fought until the end. I’m proud of the effort of the team.
“It’s a massive disappointment to all of us, especially the players. Birmingham deserved to get to extra time with the effort we put in and how smart everyone played.
“That’s the difference when you play with a team with such quality. Any chance can cost you a result. We need to congratulate Leicester because they made it through. We’re still on the build and we need to keep going.”
The Foxes will play Chelsea at home in the quarter-finals on the weekend of 21 March.