As a tune-up for Real Madrid on Wednesday this victory that takes Manchester City top, at least until Arsenal and Liverpool play on Sunday, became better and better as the game aged.

When Jérémy Doku’s jink past Fred Onyedinma caused the right wing-back to fell him in the area and claim a penalty, Manchester City were 2-0 ahead with 15 minutes left. Up stepped Erling Haaland to power the spot-kick in and the Norwegian, anonymous in Tuesday’s Champions League quarter-final first-leg 3-3 draw at the Santiago Bernabéu, had a confidence booster for the return.

Matheus Nunes, though, felt a differing emotion when a clumsy touch from Ederson’s pass outside the area ceded the ball to Ross Barkley, who, with a five a-side-style dribble, skipped in and beat City’s goalkeeper to his left.

Pep Guardiola twisted away in disgust but the concession had no material effect, Doku and Josko Gvardiol scoring further City goals, as Rodri watched from the place on the bench the midfield fulcrum had yearned for. Of those who should start against Real, Bernardo Silva, Jack Grealish, Kyle Walker, Phil Foden and, possibly, Nathan Aké had the same watching brief – and a day off, as the manager used none as substitutes.

Haaland was in the XI and 66 seconds in helped give City a lead that cast this, already, as a long afternoon for their guests. Guardiola has stated recently that the striker is not being found enough by teammates.

At Real, Kevin De Bruyne’s “vomit”, as the manager colourfully characterised it, meant he was out of the lineup. Reinstated, the Belgian’s rolling ball behind the Hatters sent Haaland galloping in. An initial attempt was saved by Thomas Kaminski and Doku’s follow-up was blocked by Alfie Doughty. The ball spiralled down towards Haaland but the volley from his trusty left foot was skewed and heading for the corner flag before pinballing painfully off Daiki Hashioka’s face, and in.

A resigned Rob Edwards, his backline already depleted by injuries, said: “We wanted to try and be aggressive and Haaland is through one on one in the first minute and he knocks [over] one of our few remaining defenders.”

Hashioka soldiered on. This was the 66th league goal his manager’s team had conceded this season. Soon, City were threatening a 67th. Gvardiol scored a screamer against Madrid and now attempted the same move inside from his left-back corridor, letting fly with the right foot that fashioned it, though this time Kaminski saved.

Gvardiol possesses an impressive technical excellence so, when De Bruyne dropped a free-kick from the right on to his head at the far post, seeing him miss the target was a surprise. It followed De Bruyne finding Haaland with a similar delivery and the 23-year-old scooping high.

At times Luton formed a six-man backline in their area yet still De Bruyne could pierce this, a pass into the sprinting Nunes teeing the midfielder up for an attempt that skimmed over Kaminski’s right post.

For some reason Julián Álvarez and not De Bruyne was on corner duty and the one from the left he dipped on to the roof netting summed up how the contest stagnated for a long phase. Another, from the right, was wasted too.

When Rúben Dias took a whack in the area the referee, John Brooks, was not interested, yet he was in a De Bruyne foul. This drew the yellow card from his pocket and provoked Guardiola – in the petty manner he can have – to “congratulate” Darren Bond, the fourth official, via placing his arms around his waist.

That it was 1-0 as the second half began pointed to City’s tepidness in front of goal. A Doku push-and-run that steered the ball out, Nunes’s hapless collapse when running in and Álvarez blazing a cross wide suggested the next 45 minutes would be a repeat.

It proved a false augury for what would end as a second-half goal rush of four. The first was from Mateo Kovacic. This time Álvarez impressed from the left corner quadrant: a quick one-two with Doku was followed by a delivery that bounced once, perfectly, for Kovacic to smash home, his right foot slicing through the ball on the right-angle.

Guardiola was delighted, but nearly saw Cauley Woodrow pull one back for the visitors immediately as Onyedinma skated around Gvardiol and found the substitute, his attempt exploding off his right boot and Ederson’s bar.

But then, after Haaland’s spot-kick and Barkley’s finish, Doku and Gvardiol markedly improved City’s goal difference. The winger cut in from the left before a finish as expert as the Croat’s, who, roving in from the same flank, beat Kaminski with a bullet from his right foot to match his effort in the Spanish capital.

Luton remain third-bottom, a point below Nottingham Forest. “Today was never going to derail us,” said Edwards, whose survival hopes rest on less taxing fixtures. “We feel that we can win enough games.”