LONDON -- At least Stamford Bridge got to see a top striker settle a big game at last.

The awkward truth for Chelsea and Thomas Tuchel is that it was Karim Benzema, a 34-year-old somehow improving with age, turning this Champions League quarterfinal tie perhaps irrevocably in Real Madrid's favour in Wednesday's 3-1 win. The France international's stunning hat trick comprised of two exquisite headers, and a reward for the sort of pressing some may think is beyond a player of advancing years.

Take your pick of Benzema's remarkable statistics: 42 goals in his last 42 games, 13 in his last seven, 10 in his last four, the fourth player ever to score back-to-back Champions League hat tricks and his tally of 11 goals in a single season is the highest by any Frenchman in the competition.

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"Every day he's better, like wine," said Madrid coach Carlo Ancelotti, who arrived in London a few hours before kick-off after testing negative for COVID-19.

Benzema is the complete striker Chelsea thought they were buying in Romelu Lukaku. His first header combined laser-like precision with sufficient power to convert Vinicius Junior's 21st-minute cross.

The second was arguably better, meeting Luka Modric's pinpoint delivery with his weight on the wrong foot yet somehow guiding a wonderful effort back across Chelsea goalkeeper Edouard Mendy.

Kai Havertz responded with a header of his own, converting Jorginho's excellent 40th-minute ball, but, less than a minute into the second half, Benzema hassled Mendy into an error, under-hitting a pass to Antonio Rudiger. Benzema beat the Chelsea centre-back in the tackle and rolled the loose ball into an empty net.

Lukaku watched all of this from the bench, omitted yet again as a consequence of Chelsea producing enough evidence over recent weeks they are currently more potent without the man acquired to make them so.

He entered the fray just after the hour mark for the anonymous Christian Pulisic and within five minutes, the contrast with Benzema was stark to the point of embarrassing.

Cesar Azpilicueta produced a left-wing cross to find Lukaku unmarked seven yards out. His header lacked conviction and drifted harmlessly off target.

"It was very important," said Tuchel of Lukaku's miss. "There are no longer away goals so if we have only a one-goal deficit or a draw, then you see the momentum is back when we score. We could have even equalise. There were a lot of spaces and chances. But the individual decisions today were far from our level of standards."

The home crowd greeted Lukaku's effort by venting their anger at a glorious chance spurned.

They are used to it by now. There was an even worse attempt a later on, hopelessly off target. In 26 minutes, he managed four touches, albeit one of those to set up Hakim Ziyech for an effort which flew just wide.

Lukaku was signed at great expense -- €115 million from Internazionale -- for a clear reason: to add ruthlessness to a team that habitually spurned too many chances.

In Tuchel's first 50 games in charge, Chelsea kept 31 clean sheets, a higher tally than any other team in Europe's top five leagues.

It was this efficiency which formed the basis of an improbable Champions League triumph last season, but this time around, given the dual mission of retaining their European crown and pursuing the Premier League title, was to align that resilience with a greater attacking threat.

Lukaku was signed as the one-man solution but the problem remains. Havertz has grown into the role of leading Chelsea's attack, at times with a strike-partner in a 3-5-2 system or alone in Tuchel's preferred 3-4-2-1, but even in their six-game winning run prior to the international break, admirable as it was given the wider uncertainty over the club's ownership and day-to-day functionality, they have often not possessed the attacking authority which could reasonably be expected of them.

Tuchel has occasionally moved to a back four in pursuit of a resolution and he appeared to regret his line-up here, withdrawing N'Golo Kante and Andreas Christensen for Mateo Kovacic and Ziyech at half-time in a series of changes to try to rectify a game slipping away from them.

Christensen was off the pace from the outset, unsettled by Vinicius' pace and sharpness of movement. Tuchel described creating that match-up with his 3-5-2 line-up as "my mistake" and even took the unusual step of turning down an easy opportunity to talk up the prospect of a second-leg revival.

Asked simply if the tie was still alive, Tuchel said: "No, not at the moment. No. We have to find our level back. I don't know where it is since the international break. The first half is a repetition of the second half against Brentford [a 4-1 home defeat] in a quarterfinal against Real Madrid. So far off our level in absolutely everything the game demands, we can't expect a result from this kind of performance.

"If we keep playing like this we will lose at Southampton and then we will get hammered at Bernabeu."

This could, of course, never be considered Lukaku's fault alone. He is merely the figurehead of a problem Tuchel has grappled with for some time, one that was exposed here by Real's superb first half display and several individual errors, none more damaging than Mendy's error within 45 seconds of the restart.

And in Lukaku's defence, none of Tuchel substitutions worked particularly well. Ruben Loftus-Cheek replacing Jorginho at the same time as Lukaku's introduction was an odd call given the Italian's importance to the team.

Reece James was understandably rusty on only his second start since December due to injury and that collective weakness on Chelsea's right flank was a vulnerability they could not mask.

In fact, the full-backs are vital to Tuchel's approach and with James clearly not at his best and Azpilicueta incapable of providing the same threat as Ben Chilwell, this is undoubtedly a contributing factor to any explanation of why the Blues struggled.

As Real's 30-something midfielder trio Modric, Toni Kroos and Casemiro all began to tire, Chelsea's perseverance created several promising positions -- Real goalkeeper Thibaut Courtois, baited throughout on his return to Stamford Bridge, made one excellent save from Azpilicueta -- but otherwise there was a lack of quality in front of goal which Tuchel will recognise all too well. Something has to change or their Champions League aspirations will be the next casualty.