Ross Barkley's lone goal in the second half was all Chelsea needed to progress to the semifinals of this year's FA Cup championship.
The 26-year-old midfielder powered the Blues to victory after converting a close-range chance from Willian's cross in the 63rd minute of the encounter at the King Power Stadium.
His goal ensured his side join the likes of Manchester United and Arsenal in the last four stage while the match between Manchester City and Newcastle United will decide the last team.
However, the west London side struggled in the opening exchanges, with the first half of the meeting with the Foxes finishing 0-0.
The hosts had a couple of scoring chances in the half which they created with headers from corners.
The restart saw a displeased Frank Lampard make three changes with Matteo Kovacic, Ross Barkley and Azpilicueta being introduced.
It was the introduction of Barkley that made the difference, with the Englishman sweeping a caress into the far corner after beautiful gameplay involving Willian and Azpilicueta.
Efforts by the home side to restore parity in the closing stages proved futile as Chelsea held on to claim a vital win.
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