Leicester sent Manchester United crashing out of the FA Cup as Kelechi Iheanacho's double sealed a 3-1 win, while Chelsea will face Manchester City in the semi-finals after beating Sheffield United on Sunday.
Brendan Rodgers' side can look forward to meeting Southampton in their first FA Cup semi-final since 1982 thanks to Iheanacho's predatory finishing at the King Power Stadium.
He put Leicester ahead in Rodgers' 100th game in charge before Mason Greenwood equalised late in the first half.
Youri Tielemans restored Leicester's lead and Nigeria striker Iheanacho wrapped up only their second win over United in 23 years and their first since 2014.
Leicester, who have never won the FA Cup and last reached the final in 1969, will head to Wembley to face Southampton in April.
United's limp exit ended their run of 29 away games without defeat in all domestic competitions since losing at Liverpool in January 2020.
Without a trophy since the 2017 Europa League, that competition is now their last realistic chance of winning the first silverware of boss Ole Gunnar Solskjaer's reign.
After reaching the Europa League quarter-finals with a win at AC Milan in midweek, Solskjaer made five changes as Paul Pogba returned to the starting line-up following his winner at the San Siro.
Solskjaer this week revealed that Fred, Bruno Fernandes and Alex Telles had played a key role in United's revival with their upbeat personalities.
But Fred had nothing to smile about as he paid the price for a woeful mistake in the 24th minute.
When Harry Maguire played a risky ball out to Fred on the edge of the United area, the Brazilian's panicked response was a weak back-pass towards United keeper Dean Henderson.
Iheanacho nipped in to intercept it before rounding Henderson and tapping into the empty net to make it eight goals in his last nine games.
United equalised in the 38th minute when Pogba's cross was cleverly dummied by Donny van de Beek and Greenwood slammed his shot past Kasper Schmeichel from 12 yards.
Lacklustre United were still out of sorts and Tielemans put Leicester back in front in the 52nd minute.
The Belgian midfielder advanced unchecked as United backed off and he took full advantage with a fine low finish from the edge of the area.
Solskjaer responded with four substitutions including the introduction of Fernandes and Edinson Cavani.
But Iheanacho killed off United in the 78th minute with a clinical header from Marc Albrighton's free-kick.
Since his first game in the FA Cup in 2016, Iheanacho has scored 13 times, more than any other player.
Chelsea set up City clash
At Stamford Bridge, Thomas Tuchel's much-changed side were below their best but still earned a potentially thrilling showdown with quadruple chasers Manchester City by beating Sheffield United 2-0.
Oliver Norwood's 24th-minute own goal, the midfielder turning Ben Chilwell's shot into the net, put them on course for the last four.
Hakim Ziyech came off the bench to finish Chilwell's pass in second-half stoppage time.
The Blues are back in the FA Cup semi-finals for a fourth time in the last five seasons after losing last year's final against Arsenal.
Chelsea won the last of the club's eight FA Cups under Antonio Conte in 2018.
"We had a good first half where we controlled everything. We lost control in the second half. After 14 consecutive matches I could feel we were tired and we made many little mistakes," Tuchel said.
Tuchel's early impact since replacing the sacked Frank Lampard in January has turned Chelsea in a rock-solid defensive unit.
The German is unbeaten in 14 games in all competitions, with Chelsea keeping 12 clean sheets in that period, including shutting out the opposition in their last seven matches.
"I could tell in training we were tired and there was a lack of concentration. That can happen sometimes. It gets harder to keep the level up," Tuchel said.