Ndidi and Gray score fantastic extra-time goals for Leicester
Foxes will travel to League One side Millwall in the fifth round
Watch clips of goals and key incidents on this page
Both sides named weakened teams (10 changes for Leicester, eight for Derby)
Have we just witnessed the start of Leicester's revival? Time will tell.
No doubt the Foxes' second string have given the ailing Premier League champions a big boost. Now we'll see if the big-name cast can pick up the baton and earn some much-needed Premier League points on Sunday.
Swansea awaits. See you then!
Leicester 3-1 Derby
Scathing from Shearer...
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Leicester 3-1 Derby
Leicester manager Claudio Ranieri on the BBC: "In this moment everything goes wrong - but tonight one thing went right.
"Derby played good football and we won. This is what we needed and I wanted. Wilfred Ndidi made a very good goal as did Demarai Gray.
"I'm happy with Ndidi. This young player full of personality and good character. We've chosen well.
"We want to do well in all competitions. We want to go forward in the FA Cup. The Premier League is not so good but we have to stay in the Premier League. This fresh air is good for the players."
Image source, APLeicester 2-1 Derby
Impact.
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Leicester 3-1 Derby
Derby manager Steve McClaren speaking to the BBC: "I don't think either team wanted a replay and we definitely didn't want extra time.
"There are some very tired players in the dressing room. It was always going to be hard work. We had a go and can't fault the players. We ran out of steam in the end.
"Tonight was about the squad - the fringe players and the injured players coming back getting a game. We missed our opportunity in the first game. I couldn't fault the players."
Image source, AFP/Getty ImagesLeicester 3-1 Derby
The Foxes know their next FA Cup fight....
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Leicester 3-1 Derby
Demarai Gray's first goal for Leicester was a belter at Old Trafford - and his first in front of his home fans wasn't bad either. Check it out...
Leicester 3-1 Derby
Martin O'Neill
Republic of Ireland manager on BBC One
It is a really big win for Leicester City - I'm delighted they've done it. I think there has been a lot of doom and gloom around the place and that will lift it.
Leicester 3-1 Derby
Leicester goalscorer Demarai Gray on BBC One: "It is nice to get on the scoresheet - it takes the pressure off us. I'm looking to score as much as possible and impact on the play."
Image source, PALeicester 3-1 Derby
Leicester goalscorer Andy King: "It was important to get a win tonight to try to kickstart some form to take into the league.
"It's been a tough few weeks and we've been getting a lot of criticism. Tonight we showed the fight we have got in the squad.
"We have 14 massive games left in the league but now we are through in a couple of rounds of the cup. Why can't we create another journey this season?"
Leicester 3-1 Derby
Kevin Kilbane
Former Everton winger on BBC Radio 5 live
We were looking where the spark was going to come from. Gray provided that spark for the Leicester opener and then Ndidi and Gray scored those great goals.
I think Leicester could spark the season. Can he get more game time? Can he play more central?
Image source, PALeicester 3-1 Derby
Demarai Gray takes most of the plaudits as he shakes hands with team-mates and opponents at the whistle. How is he not starting every week for the Foxes?
Leicester 3-1 Derby
No more drama. Leicester are through to the last 16!
Image source, APLeicester 3-1 Derby
One more minute on the clock...
Leicester 3-1 Derby
Leicester 3-1 Derby
Derby are still plugging away, but they're not going to pull this one back. To paraphrase someone quite well known, if they win it then I'll present my next live text in my pants.
Leicester 3-1 Derby
The feelgood factor has returned around the King Power Stadium for the first time in a while. The home fans cheering every pass now, and enjoying giving pelters to their friends from Derby.
Leicester 3-1 Derby
Claudio Ranieri is smiling again!
Leicester 3-1 Derby
Kevin Kilbane
Former Everton winger on BBC Radio 5 live
That was a special goal. He's been superb tonight. As soon as he gets Richard Keogh backed up in the area, he checks inside him and Matej Vydra, and then has the technical ability to guide the ball past keeper Jonathan Mitchell.
Image source, PA
Demarai Gray
Someone has just opened the top drawer...
Demarai Gray pulls out a moment of magic to put Leicester City into the fifth round. The winger slaloms past Derby defenders like they're markers on a ski slope, keeping his composure to rifle in an angled drive high into the onion bag.