Chelsea's hopes of salvaging success from a season of abject mediocrity were ended ruthlessly by Real Madrid as the holders advanced into the Champions League semi-final at Stamford Bridge.
The Blues were always battling against the odds to overturn a 2-0 deficit from the first leg in the Bernabeu and their cause was not helped by a familiar failing as a battling performance was undermined by missing a succession of clear chances.
N'Golo Kante missed a glorious first-half opening while Marc Cucurella was blocked by former Chelsea keeper Thibaut Courtois when he looked certain to reduce Real's advantage.
The Spanish champions had moments of their own and there are few sides more adept at making opponents pay for wasted opportunities and so it proved.
A lightning counter attack led by Vinicius Junior ended with Rodrygo putting the tie to bed with a close-range finish just before the hour
The Brazilian forward then walked in the second after brilliant, unselfish work by Federico Valverde with 10 minutes left.
Carlo Ancelotti's quest for an historic fifth win as a coach in this tournament will continue with a semi-final against either Bayern Munich or Manchester City while Chelsea's interim manager Frank Lampard, who now has four defeats from four games, must somehow lift the grim mood of despair around the club.
Chelsea flaws exposed again
Chelsea have failed to score in four of their 10 games - only FC Copenhagen (5) have failed to score more often in the Champions League this seasonIn among the many mistakes made by Chelsea's new ownership group led by Todd Boehly, one of the most obvious is shelling out £600m in a madcap transfer spree but failing to acquire someone who deals in the most precious commodity of all, namely goals.
Chelsea gave a very decent performance here, certainly the best of Frank Lampard's short reign, but a painful lack of end product meant there was almost an air of inevitability they would eventually be punished by the street wisdom and quality in Carlo Ancelotti's side.
Kante had Chelsea's best opportunities while Cucurella and substitute Mykhailo Mudryk also failed to cash in on good positions, although the latter's chance came with only minutes left and the tie over.
Chelsea are currently languishing in 11th place in the Premier League. They will not be in the Champions League next season, a big pull for potential purchases, while Boehly and the Clearlake group must find a manager to mend the fractures in the club after the sackings of Thomas Tuchel and Graham Potter this season.
It will have to be ambition and reputation that lures that man because all the elite names who may come into contention will invariably wish to ply their trade in the Champions League.
Lampard will need to show some serious powers of motivation to inspire an upbeat end to the season at a club that has lost its way.
Real on the march again
Rodrygo (centre) scored the goals to seal the tie, but midfielder Federico Valverde (second from left) was the standout performerReal Madrid's reign as the kings of Europe continues into another Champions League semi-final and they will pose a massive threat to whoever they meet - most likely Manchester City as they hold a 3-0 advantage from the first leg against Bayern Munich.
They not only have the competition's most successful manager in four-time winner Ancelotti but possess a team of such vast experience that knows exactly how to get the job done.
Chelsea followed Liverpool in being put away in the Champions League with the minimum of fuss.
Real are always able to find a hero from somewhere when it matters and here it was Rodrygo with two simple finishes, although man of the match was the outstanding Uruguayan Valverde.
This is a club that always believes it is their destiny to win the Champions League and they will be getting the old familiar feeling as they move into the last four once again.
Player of the match
RodrygoRodrygo
Chelsea
Squad number7Player nameKanté
Squad number6Player nameThiago Silva
Squad number24Player nameJames
Squad number1Player nameArrizabalaga
Squad number5Player nameFernández
Squad number8Player nameKovacic
Squad number33Player nameFofana
Squad number23Player nameGallagher
Squad number29Player nameHavertz
Squad number32Player nameCucurella
Squad number14Player nameChalobah
Squad number19Player nameMount
Squad number11Player nameJoão Félix
Squad number15Player nameMudryk
Squad number17Player nameSterling
Line-ups
Chelsea
Formation 3-4-2-1
1Arrizabalaga
14Chalobah6Thiago Silva33Fofana
24James5Fernández8Kovacic32Cucurella
7Kanté23Gallagher
29Havertz
1Arrizabalaga14Chalobah6Thiago Silva33Fofana24JamesBooked at 50mins5FernándezSubstituted forSterlingat 67'minutes8Kovacic32CucurellaBooked at 34minsSubstituted forMudrykat 68'minutesBooked at 89mins7Kanté23GallagherSubstituted forJoão Félixat 67'minutes29HavertzSubstituted forMountat 77'minutesSubstitutes
10Pulisic11João Félix12Loftus-Cheek15Mudryk16Mendy17Sterling19Mount20Zakaria22Ziyech28Azpilicueta30Chukwuemeka67HallReal Madrid
Formation 4-3-3
1Courtois
2Carvajal Ramos3Militão4Alaba12Camavinga
15Valverde8Kroos10Modric
21Rodrygo9Benzema20Vinícius Júnior
1Courtois2Carvajal RamosSubstituted forNachoat 82'minutes3MilitãoBooked at 21mins4AlabaSubstituted forRüdigerat 45'minutes12Camavinga15Valverde8KroosSubstituted forCeballosat 76'minutes10Modric21RodrygoSubstituted forAsensioat 81'minutes9BenzemaSubstituted forTchouaméniat 71'minutes20Vinícius JúniorSubstitutes
5Vallejo6Nacho7E Hazard11Asensio13Lunin16Odriozola17Vázquez18Tchouaméni19Ceballos22Rüdiger24Mariano26López AndúgarReferee:Daniele OrsatoAttendance:39,453Live Text
Match ends, Chelsea 0, Real Madrid 2.
Second Half ends, Chelsea 0, Real Madrid 2.
Attempt saved. Dani Ceballos (Real Madrid) right footed shot from the left side of the box is saved in the centre of the goal. Assisted by Federico Valverde.
Mateo Kovacic (Chelsea) wins a free kick in the defensive half.
Foul by Vinícius Júnior (Real Madrid).
Hand ball by Wesley Fofana (Chelsea).
Attempt missed. João Félix (Chelsea) right footed shot from outside the box is too high. Assisted by Mateo Kovacic.
Mykhailo Mudryk (Chelsea) is shown the yellow card for a bad foul.
Foul by Mykhailo Mudryk (Chelsea).
Luka Modric (Real Madrid) wins a free kick in the defensive half.
Offside, Chelsea. Mason Mount tries a through ball, but Mykhailo Mudryk is caught offside.
Offside, Real Madrid. Marco Asensio tries a through ball, but Vinícius Júnior is caught offside.
Foul by Mykhailo Mudryk (Chelsea).
Nacho (Real Madrid) wins a free kick in the defensive half.
Mateo Kovacic (Chelsea) wins a free kick in the defensive half.
Foul by Vinícius Júnior (Real Madrid).
Raheem Sterling (Chelsea) wins a free kick in the defensive half.
Foul by Eduardo Camavinga (Real Madrid).
Attempt saved. Mykhailo Mudryk (Chelsea) right footed shot from the left side of the box is saved in the centre of the goal.
Attempt blocked. João Félix (Chelsea) left footed shot from the left side of the box is blocked. Assisted by Mateo Kovacic.