While Leroy Sané, Yaya Touré, David Silva and Sergio Agüero jostled for Manchester City’s man-of-the-match award, Brad Guzan’s status as Middlesbrough’s outstanding individual brooked absolutely no argument.

Aitor Karanka’s goalkeeper performed wonders to keep the scoreline respectable on a day when Pep Guardiola’s side warmed up for Wednesday’s Champions League trip to Monaco by extending their unbeaten run to 11 games as they coasted into the semi-finals.

If the visiting performance was surely good enough for Guardiola to temporarily forget his strained relationship with Karanka – something stemming from their respective Barcelona/Real Madrid pedigrees and associations with a certain José Mourinho – Boro’s manager can expect awkward questions about his job security to resurface.

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As much as the Basque’s relegation-threatened players are probably best served by being out of the FA Cup, the home manager – who had threatened to offer Guardiola a post-match glass of cut-price cava – will be deeply concerned by yet another game in which his side failed to score, were thoroughly outclassed and displayed strictly limited fighting spirit.

Terrorised by Sané’s mesmerising wing play, Boro conceded midfield to the at times imperious Touré and never fully fathomed the elusive movement of Agüero and Silva as City recorded a third straight clean sheet.

“When you attack good, you defend good,” said Guardiola, his credo apparently vindicated. “We defend 40m away because I always believe that when the ball is far from our goal, we’re safe. The reason we’re creating more goals and conceding fewer is the way we play.”

Touré jokes that his Catalan manager has gone from dubbing him the squad’s “uncle figure” to applying the label “grandfather” but all that experience came in handy in the third minute when City’s veteran midfielder spotted the excellent Pablo Zabaleta overlapping from right-back and lofted a pass in his direction.

With Karanka’s defence caught uncharacteristically cold, Zabaleta was able to cushion a cross towards Raheem Sterling and, although he misjudged that delivery, Silva was lurking, unattended, just behind him and duly delighted in flicking out his left boot and beating Guzan courtesy of a close-range volley.

A team very much designed to defend, Boro are not great at coming up with Plan Bs and, sure enough, they struggled to get going. It was the sort of situation in which Stewart Downing might have been a useful individual for Karanka to deploy – but along with Patrick Bamford, the former England winger was excluded from the squad. Indeed it seems doubtful either player will feature again this season.

If Downing has not always been exactly a Karanka favourite, Álvaro Negredo and Gastón Ramírez found themselves on the bench following some substandard performances.

An injury to Gestede dictated that Negredo, a former City striker, came on midway through the first half – but not until the former had connected with Grant Leadbitter’s corner and prompted a embarrassing fumble on Claudio Bravo’s part before Zabaleta came to the rescue and scooped the ball clear.

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Philosophy – the whole sweeper/keeper thing – explains why Guardiola jettisoned Joe Hart for Bravo and, perhaps with that error having jogged a few memories, Boro belatedly set about testing the vulnerabilities in this belief system. For a little while, they succeeded in pressing City high up the pitch, preventing them from passing out from the back and slowing their initially rapid tempo.

A spell in which the game became unexpectedly scrappy ensued but with Sané’s pace persistently troubling Antonio Barragán, it could not last. Accordingly, Touré really should have made it two after meeting Kevin De Bruyne’s free-kick but, instead, headed wide.

Meanwhile, Leadbitter – subsequently replaced by Ramírez –had Mike Dean’s leniency to thank for keeping him on the pitch when he tripped Touré shortly after collecting a yellow card for lunging at De Bruyne.

Boro lived similarly dangerously when an equally frustrated Adam Clayton got away with an apparent stamp on Sterling. It possibly reflected the Teessiders’ sense of powerlessness as Silva shot narrowly over and Agüero deceived young Dael Fry – on for the injured Bernardo – before seeing a shot rebound off the inside of a post after being deflected on to the woodwork by Guzan’s foot.

Marten de Roon escaped unpunished after flinging out an arm and catching Nicolás Otamendi on the back of the head in another cameo emphasising Boro’s struggles to second-guess their guests.

While Guzan did well to palm a shot from the latter away from the corner – “He was perfect,” enthused Karanka – the American had no answer to Sané’s subsequent thoroughly startling change of pace and his fabulous, beautifully weighted, low cross, which enabled Agüero to guide a six-yard shot home.

“I’m delighted,” said Guardiola. “We’re so, so, happy to be in the semi-final.”