Carlo Ancelotti is all about poise under pressure and, perhaps tellingly, the Italian lost his composure only once as he made it six points out of six since taking charge at Everton.

After misunderstanding a question about Moise Kean he, albeit briefly, looked distinctly uncomfortable when quizzed on the forward’s perceived shortcomings. “Oh, I thought you were asking me about David Moyes,” said Ancelotti laughing, after an Italian journalist explained the confusion, paving the way for an explanation of the thinking behind Kean’s replacement with Fabian Delph in one of those decisions that demonstrated why Ancelotti is paid a reputed £12m a year.

Delph’s introduction to reinforce a midfield that had turned ragged increased Everton’s possession and control, prefacing Dominic Calvert-Lewin’s third goal in two games. “Delph helped us a lot,” said Ancelotti. “After playing for Manchester City he’s used to keeping possession under pressure.”

At a juncture when Fabian Schär had just equalised for a resurgent Newcastle and the increasingly irrepressible Andy Carroll was winning almost everything in the air, the newcomer certainly altered the narrative. It was the sort of game that Marco Silva’s Everton tended to lose but an amalgam of Ancelotti’s clarity of tactical thought and Calvert-Lewin’s new-found ruthlessness left Steve Bruce’s spirited side pointless.

“We suffered a lot,” acknowledged Ancelotti. “We lost control after 25 minutes but it was difficult to avoid Newcastle’s pressure.”

Although Newcastle played well at times, the fatigue stemming from festive fixture overload ensured Bruce’s players made their fair share of mistakes in a game littered with errors. The first came within seconds when Miguel Almirón should arguably have collapsed under considerable pressure from Michael Keane’s arm after being put through on goal by Joelinton but instead stumbled before shooting wide. A potential penalty and red card at that point could have set a very different tone but, instead, Ancelotti merely wagged a disapproving finger. Suitably warned, Everton swiftly looked considerably slicker, sharper and speedier than their hosts and few were startled when Calvert-Lewin scored his second goal in three days.

It arrived when the fallout from Gylfi Sigurdsson’s initially blocked free-kick was deflected into the path of the striker, whose close-range shot evaded Martin Dubravka’s reach. No matter that it was all a bit scruffy; Duncan Ferguson celebrated as if it were a cup-winning goal he had scored himself. As Ancelotti kept his cool, standing impassively on the edge of the technical area, his assistant bounded past him, almost knocking the manager over as, arms aloft, he burst out of the dugout and on to the pitch.

Everton manager Carlo Ancelotti watches on. Photograph: Scott Heppell/Reuters

Unlike Ancelotti’s No 2, Carroll is a far-from retired throwback centre-forward and, by way of proving it, almost singlehandedly dragged Newcastle back into things, disrupting the growing visiting dominance while setting teammates a toweringly defiant example. Whereas previously it had been all about Theo Walcott’s menacing advances and Kean’s excellent movement, suddenly Carroll was here, there and everywhere, making vital interceptions at both ends and raising Joelinton’s game to new heights along the way.

Everton’s penalty area was subjected to a sustained attacking assault with Jordan Pickford – as a former Sunderland goalkeeper, the afternoon’s pantomime villain – doing well to palm Schär’s high-velocity shot to safety. Ancelotti had much to contemplate as he dug his hands deep into the pockets of his classically tailored dark overcoat, particularly after Carroll – who else? – rose imperiously above all-comers to head Jetro Willems’s free-kick down for Schär to volley beyond Pickford.

Everton’s manager responded by introducing Delph and the latter’s solidifying presence offered the Merseysiders a counterattacking platform, providing a superb springboard for Richarlison’s exceptional pace. When Carroll conceded possession it was Delph’s neat pass under pressure that initiated the break from which the visitors restored their lead. That move concluded with Richarlison crossing superbly for Calvert-Lewin, whose sliding, slightly scuffed, close-range connection prefaced goal number two, thereby suggesting he is finally discovering the end product to match wonderful aerial prowess and fine technical ability.

“Dominic must improve,” said Ancelotti, cautiously. “But he has all the qualities to be a top striker.”