Chelsea are seeking to enhance their Premier League top four prospects after a rare header from Pedro secured their FA Cup semi-final place.
Alvaro Morata's first goal of 2018 was cancelled out by Jamie Vardy to force extra-time at Leicester.
And Pedro planted a header beyond Kasper Schmeichel to earn a 2-1 win and a last-four bout with Southampton.
First, following the international break, Chelsea play Tottenham on April 1 eager to narrow the gap to their rivals.
The fifth-placed Blues trail Spurs, in fourth, by five points with eight games to go and the prize of a Champions League berth at stake.
"It's very strange to score with the head," Pedro said.
"It's good for my confidence in the team and to help us pass to the next round of the FA Cup.
"We are in a difficult situation in the league but in the FA Cup we are in the semi-final against Southampton.
"It's an opportunity for us to go to the final and help us fight until the end for the top four."
N'Golo Kante, who provided the assist for Pedro as part of an all-round superb display, was pleased with Chelsea's reaction after a week which saw them exit the Champions League at Barcelona.
"I'm happy. In the league it's a little bit difficult. (And) we are out of the Champions League," Kante said
"It was important for us to go to the semi-final. We achieved this and we have to go to the final. This is our target.
"This week we played in the league and won against Crystal Palace, we were unlucky against Barcelona and we have this win. We have to recover and change our minds and when we come back go strong until the end of the season."
Foxes midfielder Marc Albrighton rued a "missed opportunity".
The FA Cup is the one domestic trophy which has proved elusive, after the Premier League triumph of two seasons ago. Four times the Foxes have finished as runners-up.
Albrighton said in the Leicester Mercury: "It feels like an opportunity missed. It is something we looked at before and targeted. We said we have a massive chance here.
"We are very frustrated because we felt we deserved a lot more out of that.
"For large parts of the game we dominated and had enough chances and just a lapse of concentration and we let them in for the winner in extra time.
"It is always difficult to come back in extra time after conceding."