Leicester boss Brendan Rodgers vowed to keep chasing the top six after the win over Crystal Palace.
Ademola Lookman and the impressive Kiernan Dewsbury-Hall scored in the first half to win 2-1.
Wilfried Zaha recovered a goal after Kasper Schmeichel saved his penalty. The goalkeeper had already denied the striker from the penalty spot but VAR had ruled that he had invaded Caglar Soyuncu.
The Foxes sit ninth in the Premier League, 11 points behind sixth-place West Ham with three games remaining, and Rodgers refused to give up the hunt.
He said: “We can’t stop until the last whistle, we’ve been really unlucky and it’s been a real challenge for us without our best players. Now they’re coming back and because they’re back it means I can get some rest and put on a fresh team.
“It is going to be a great challenge because we are playing from start to finish and we are going to fight until the end.
“I thought Kiernan was outstanding. He is a young player who since he came to the team is everything that represents a team of mine. Honest, great industry, he runs, works, presses and has quality.
“We told him, as number eight, the job is to create goals and score goals and he made a beautiful pass for Ade’s first and the second goal he scored was top notch.
“He has made a real impact with his honesty and quality and I am delighted for him.”
Leicester survived a couple of early scares when Zaha fired wide before Jean-Philippe Mateta tested Schmeichel after 18 minutes and Joachim Andersen headed the resulting corner wide.
That was for the best for Palace in the first half as the Foxes, fueled by Dewsbury-Hall, took control.
He opened the scoring six minutes before the break when Youri Tielemans found the midfielder who produced an excellent pass to Lookman.
He cut inside Andersen to bury his seventh of the season and end an eight-game wait for a goal.
Then, just before the break, Dewsbury-Hall added a brilliant second.
Much was due to Marc Guehi’s mistake when he let the ball pass underfoot for Patson Daka to cross to Dewsbury-Hall. The midfielder then held off Cheikhou Kouyate and deflected a brilliant shot past Vicente Guaita from the edge of the area.
It was a long way back for Palace and Guaita deflected Tielemans’ shot, but they got a life saver when Tielemans tripped Jordan Ayew in the box after 64 minutes.
Zaha’s terrible penalty was saved by Schmeichel low to his left only for VAR to order a replay as Soyuncu invaded.
Zaha went the other way but was saved again by Schmeichel but the ball fell to the striker for a header.
However, he failed to get Palace back on their feet and they fell behind the Foxes in the Premier League.
Boss Patrick Vieira said: “The performance, in the first half, Leicester were the better team and they started with better intentions. We didn’t risk enough to find our midfield three.
“We didn’t compete well enough and they were more aggressive. In the second half we created some chances but it was too much for us to climb.
“The difficulty was conceding the second goal just before the break. In general, it was not a good performance from us.
“It is important for me and for the club to be consistent with our emotions. There are still many details that we need to improve and some of them will come with time.