|Real Madrid beat wasteful Chelsea to reach Champions League semis, Source: youtube/ FPT Bong Da |
The home team, with Frank Lampard back in the dugout for a second spell, came into the match at Stamford Bridge with form and history against them.
They started brightly but rued a number of huge missed chances that would have heaped pressure on the defending champions.
The Spanish giants made Chelsea pay for their profligacy when Rodrygo scored in the 58th minute after a speedy counter-attack and he made it 2-0 with 10 minutes to go.
"We suffered a lot and helped us stay at 0-0 at the end of the first half," Real Madrid boss Carlo Ancelotti told BT Sport.
"Second half we were much better and scored the two goals. We are happy to have qualified."
Chelsea, the 2021 European champions, have now lost all four of their matches since Lampard returned to the club as caretaker boss earlier this month in place of the sacked Graham Potter.
Lampard, who also managed the club from 2019 until early 2021, bemoaned his team's profligacy.
"We played really well for 60 minutes," he said. "We created chances but you have to take them."
The former Chelsea midfielder said his men must find motivation from playing for the club as they contemplate a bleak final few weeks of the season.
"You're playing for Chelsea," he said. "So regardless, every game you play you have to give everything. I won't let anyone off the hook and we have to show. That standard cannot drop."
Ancelotti stuck with the same team that won the first leg 2-0 last week while Chelsea caretaker boss Lampard restored Reece James, Mateo Kovacic and N'Golo Kante to his line-up.
Roared on by an expectant crowd despite their current woes, the home side made a good start against the 14-time winners.
- Chances -
They had a glorious chance to take the lead but Kante skewed his left-foot shot wide from about 12 yards.
The visitors, content to bide their time, looked sharp on the break.
Midway through the opening period Rodrygo created space for himself and thumped an effort against the outside of the post from an acute angle while Luka Modric tested Kepa.
But Chelsea should have been ahead on the stroke of half-time when James fizzed a ball across the box from the right and it fell to Marc Cucurella at the back post.
The defender took a touch and shot but Thibaut Courtois came flying out of his goal to save.
Kante had another golden opportunity to take the lead early in the second half but his close-range effort hit Eder Militao and deflected away to safety.
Real took the wind out of Chelsea's sails with just over half an hour to go, when Rodrygo scored from close range after an assist by Vinicius Junior.
Lampard made a number of attacking substitutions, bringing on Raheem Sterling, Joao Felix and Mykhailo Mudryk in a desperate bid to get back into the match.
But Rodrygo found the net again in the 80th minute, tapping home after a clever assist from Federico Valverde.
Real Madrid will likely play Manchester City in the semi-finals, with Pep Guardiola's team 3-0 up against Bayern Munich after the first leg of their last-eight tie.
Former Chelsea boss Ancelotti is chasing a record-extending fifth win as a coach in the tournament.
But Chelsea, used to winning silverware over the past two decades, are contemplating the final stretch of a horrendous campaign despite a staggering spend of more than £500 million ($621 million) in the first year of the club's new ownership.
Trophyless this season, they are languishing in 11th in the Premier League and look unlikely to qualify for European football next season.
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Atalanta slipped up in their bid to reach next season's Champions League after being held 1-1 at Fiorentina in Serie A on Monday.