If this showed why Everton hired Sam Allardyce, the reasons for his recruitment were confirmed at a stroke. The 63-year-old may be a one-man guarantee against relegation but his new team now reside in the top half of the table. Perhaps panic, rather than necessity, accounted for his arrival, but this debut win had the stamp of classic Allardyce.

“The fans, players, staff and owners can breathe a little easier,” said the first man to manage seven Premier League clubs after offering a snapshot of why the previous six had deemed him eminently employable. There was Allardyce’s trademark clean sheet, already equalling the tallies his predecessors, Ronald Koeman and David Unsworth, managed in the league, even if Huddersfield’s drought on the road, which dates back to their opening-day win at Crystal Palace, helped account for it.

“Defensively did Huddersfield have a chance today?” asked Allardyce, aware of the answer to his own question. “That gave us a platform to go on and win the game.”

He has long shown a capacity to win the winnable games, and home matches against promoted clubs on losing runs belong firmly in that category. “It is not about four losses in a row,” insisted the Huddersfield manager David Wagner. “Every game has its own story.”

But this was a sequel in the Allardyce saga. Few have procured more points from forgettable fare. “It could have been better for entertainment, more passing and moving, but we can build on that as we go on,” he said. Allardyce’s reputation for ugly effectiveness precedes him. He is likely to keep Everton up and it probably will not be pretty. One high-class goal was out of keeping with a low-calibre game. The pragmatist in Allardyce was never going to reject another that contained an element of luck.

Equally, the opener illustrated the latent talent in Everton’s ranks. Cuco Martina recorded their first shot on target under the new manager. It was also the only one before the interval. Then came Allardyce’s first decisive intervention; Aaron Lennon and Gylfi Sigurdsson were ordered to stay further upfield. The Icelander, who had looked anything but a £45m player before then, duly delivered his most meaningful goal since his club-record transfer from Swansea. Wayne Rooney instigated the move, picking out Dominic Calvert-Lewin, who pierced the offside trap with a backheel flick for Sigurdsson to convert.

Wayne Rooney impressed as Sam Allardyce’s on-field lieutenant for Everton. Photograph: Jan Kruger/Getty Images

Everton soon acquired a taste for backheel flicks. Lennon released Calvert-Lewin with another, Jonas Lössl parrying the striker’s shot. With Huddersfield now committing more men forward, they were caught on the counterattack. Rooney sent Calvert-Lewin running clear and the 20-year-old’s shot was deflected over Lössl by the unwitting Mathias Jorgensen.

It meant the stand-in captain and youthful centre-forward were involved in both goals. While a less garlanded figure in the No10 shirt, Huddersfield’s Aaron Mooy, was the game’s outstanding individual in the first half, Rooney grew in influence. He was Allardyce’s on-field lieutenant, enforcing positional discipline as he barked orders. Everton were at pains to ensure they were not caught with too many men ahead of the ball. Indeed, Allardyce suggested they were initially too cautious, too scarred by past defeats.

The newcomer retained the personnel that Unsworth, now happily ensconced in the directors box, selected for the 4-0 win over against West Ham, but a 4-3-3 formation that became 4-5-1 out of possession was familiar to long-time Allardyce-watchers. Less typical, given his emphasis on dead-ball situations, were some wretched set-pieces from Sigurdsson.

It is easy to imagine where Allardyce’s attention may be concentrated. He and Everton have the feel of a marriage of convenience. Their circumstances produce strange bedfellows. There was the incongruous sight of Bill Kenwright, the committed Evertonian, hugging the Liverpool loyalist Sammy Lee, who has joined Allardyce’s backroom staff. Both had the sense not to embrace the nearby Duncan Ferguson.

There were no choruses of Allardyce’s name, except when the Huddersfield fans chanted first that Wagner was better and then thinner than his Everton counterpart. Allardyce nonetheless described his reception as “brilliant” and he got a louder welcome before kick-off than Speedo Mick, a fundraising Everton fan who appeared on the pitch in the swimming trunks that account for his nickname.

If Everton were sinking, Allardyce was appointed precisely because he can get imperilled teams buoyant again. His impact is apparent already.