Chelsea booked their fourth FA Cup final appearance in five years and ended Manchester City's hopes of winning four trophies this season with a 1-0 win at Wembley.
Hakim Ziyech's 55th-minute goal separated the two sides, but Manchester City rarely troubled their rivals and coach Pep Guardiola will be worried after seeing Kevin de Bruyne limp off with an ankle injury shortly after the start of the second half.
Leicester City face Southampton in the second semi-final on Sunday afternoon.
West Ham United's hopes of a top-four finish suffered a setback when they lost a thrilling game 3-2 away to Newcastle United, who in turn take a huge step towards assuring top-flight survival.
The game turned in the 36th minute when Issa Diop scored an own goal and Craig Dawson was sent off for a second yellow card.
Joelington doubled Newcastle's lead before the break, but Diop led a brave West Ham fightback with a goal in the right net in the 73rd minute, before Jesse Lingard's 80th-minute penalty levelled the scores.
However, Newcastle substitute Joe Wilcock sealed three vital points with a powerful header just moments after getting into the game in the 82nd minute.
Gylfi Sigurdson and Harry Kane both scored twice as Everton and Tottenham drew 2-2 on Friday night in a result that does nothing for either side's European ambitions.
Worryingly for Tottenham, Kane had to limp off with an ankle injury which makes him a serious doubt for next weekend's Carabao Cup final.
Sheffield United's relegation was confirmed with a 1-0 defeat away to Wolves. Willian Jose's first goal for Wolves in the 59th minute leaves Sheffield 19 points from safety with just 18 left to play for.
Norwich City will replace Sheffield in the top-flight next season when they became the first team to be promoted to the Premier League from the Championship this season after Swansea and Brentford failed to win their respective games.
It is the fourth time the club from the southeast of England has won promotion in a decade.
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