A 1-1 draw in the Spanish capital still gives the Blues the upper hand thanks to their away goal, but Thomas Tuchel's men could have had a much more convincing advantage but for a tale of two strikers.
In a story of his first season at Chelsea, Timo Werner missed a glorious chance to put his side in front early as the outstretched leg of Madrid goalkeeper Thibaut Courtois denied his old club.
That miss even provoked criticism from the wife of Werner's teammate Thiago Silva.
"Every team I go to there is a striker who keeps missing goals," Isabelle da Silva posted in a since deleted Instagram message.
At the other end, after Christian Pulisic had put Chelsea in front, Karim Benzema needed barely a half-chance to blast Real back on level terms for his 28th goal of the season and become the joint fourth highest goalscorer in Champions League history.
Those are the sorts of numbers Chelsea expected when they paid £47 million ($65 million) for Werner last June at a time when other clubs, including Madrid, were scrambling to find the money just to pay their players as the coronavirus pandemic halted football across Europe.
Backed by Russian oligarch Roman Abramovich, Chelsea were the club least deterred by the pandemic as they splashed out a total of £220 million in the transfer market last summer.
That expense has been rewarded by a return to the last four of the Champions League for the first time in seven years.
Yet, none of the attacking trio of new signings, Werner, Kai Havertz and Hakim Ziyech have consistently shown their best form.
Havertz and Ziyech started the first leg on the bench, but Tuchel has remained loyal to Werner since taking charge in January despite his lack of goals.
The German international has scored just three times in his last 38 games for club and country, one of which came against fourth-tier Morecambe in the FA Cup.
Tammy Abraham has been linked with a move away from west London due to his limited opportunities under Tuchel, while 34-year-old Olivier Giroud is out of the contract at the end of the season.
The need for a prolific goalscorer to back up the significant defensive improvement since Tuchel replaced Frank Lampard has even sparked rumours Abramovich could be forced to spend big again.
Chelsea are among a number of clubs interested in Borussia Dortmund's Erling Haaland.
But Tuchel remains confident that Werner can prove to be the consistent finisher the club need.
"You will not find one manager who will not add a 20-goal striker to his squad. I cannot have enough of them, if you can guarantee that," said Tuchel when asked about interest in Haaland.
"But this is what Chelsea bought, they bought Timo Werner and he is a 20, 30-goal striker a year. Now he is struggling a little bit, for the first time in his career.
"In any transfer, there are risks of adaptations, change of country, change of mentality. It needs time. It's not a puzzle where you identify one piece and you go out and find the exact piece, it's more than that and that's why there is no rush and no panic."
There have been bright moments in the 25-year-old's difficult first year in England.
His slick pass into Havertz for his second goal in a 2-0 win over Fulham on Saturday took Werner's tally for assists for the season to 10, to compliment his 11 goals.
But he desperately needs a big moment to quieten his doubters.
The chance to knock Real Madrid out in the Champions League semi-finals is the perfect stage to prove his worth.