Two consecutive victories for the first time this season: Erik ten Hag is engineering the U-turn Manchester United require. But to have as many wins – four – as defeats shows the work still to do for the manager.

The holders of the League Cup had not gone out in the third round since Swansea were beaten in September 2013. So after winning at Burnley on Saturday a loss to this much-changed Crystal Palace would have revived the torrent of analysis aimed at Ten Hag before facing the same opposition here in Saturday’s league meeting.

This did not occur. Instead, United performed with a swagger that will please the manager as much as André Onana’s alertness when he was finally called upon to do what he is paid for: make a save – the Cameroonian sharply using a leg to repel Jean-Philippe Mateta’s effort.

This was Palace’s opening shot on target and came in the 69th minute, underlining just how dominant their host was.

From early on, the possession style Ten Hag wishes to play was in evidence as United fanned out in Palace’s half and tapped the ball about, forcing their opponents to give chase.

A Mason Mount flick to Casemiro had the Brazilian drilling a pass into space for Anthony Martial but the striker’s anticipation failed him. Then Harry Maguire, in his first start this term, displayed plenty of quality when cutting out a dangerous Jeffrey Schlupp cross as it fizzed across United’s area.

Ten Hag configured his players in a nominal 4-2-3-1 that switched to 4-1-4-1 in attack – Mount becoming the extra advanced operator. The manager made seven changes from the win at Burnley yet still had an XI that featured Sofyan Amrabat (on full debut), Alejandro Garnacho, Mount and Onana. Roy Hodgson’s shuffle of his Palace pack came up with eight new names. Two of the biggest – Eberechi Eze and Marc Guéhi – were on the bench in what seemed a quasi-white flag move from the manager regarding progress in the competition.

After 18 minutes the United old boy, Dean Henderson, had to be replaced by Sam Johnstone, after the goalkeeper appeared to injure himself taking a long kick down field. Johnstone’s first act was to concede and it was simple for United: Mount dropped the ball to Facundo Pellistri on the right, the winger rolled it inside for Diogo Dalot and his buccaneering run allowed him to spin a cross over the turf where Garnacho slid in, firing a shot to Johnstone’s left.

Alejandro Garnacho puts Manchester United ahead

Alejandro Garnacho fires a shot past the Crystal Palace defender Nathaniel Clyne to put Manchester United ahead. Photograph: Dave Thompson/AP

Fast forward a minute and the newly arrived keeper was beating out a fierce Dalot shot as United looked to kill off Palace as soon as possible. Next Pellistri, played in by Garnacho, pulled the trigger at close range and only a desperate Chris Richards– via a hook of a leg – thwarted him.

A corner was the result and United doubled their lead. Mount swung it in from the right and Casemiro – as he has a penchant for doing – rose and headed home. By half-time United were playing a back-three at times, Casemiro reversing to become the middle defender and Amrabat taking up his place. This, in microcosm, showed their confidence and control.

Before the second half Mount was removed by Ten Hag for Victor Lindelöf, the Swede deployed as an inverted centre-back. He launched one surging run that swept him deep into Palace territory, swapped passes with Martial, but the return ball from the French forward went awry.

In a snapshot of how Ten Hag will deploy Amrabat when possible, the Moroccan was placed alongside Casemiro in a midfield fulcrum that oozed poise and craft. United’s third goal contained each of these and starred the former Real Madrid man. From an inside-right berth, Casemiro spiralled a classic schemer’s lob to the back post for the predatory Martial to fire the ball past Johnstone with a swish of his left boot.

Tie over and the cup defence up and running for Ten Hag’s team who had earned the right to strut about their famous home as they now did.

When Hannibal Mejbri was taken off Ten Hag threw a dazzling smile at the 20-year-old who had been excellent in an advanced role. Martial received the same reception when making way for Rasmus Højlund: it was this type of night for United.