One banner called for Sam Allardyce to go at Goodison Park but Theo Walcott’s sharp finish shielded the Everton manager from further hostility. Those wishing to register distrust in the former England manager’s style must make do with a club survey for now.

Walcott’s third Everton goal since arriving from Arsenal in January lifted an otherwise grim affair and Everton to eighth in the Premier League as Newcastle’s winning streak came to a subdued end. Rafael Benítez and his players have defied expectations to haul themselves clear of relegation danger but a lack of quality in attack was glaring.

Newcastle finished on top, preying on Everton’s anxieties, having a handball claim against Phil Jagielka dismissed and almost equalising in the final seconds only for Seamus Coleman to intercept Jacob Murphy’s cross towards Dwight Gayle with a superb header.

Benítez claimed Bobby Madley was too lenient with Everton’s physical approach but accepted that, in Walcott and Wayne Rooney, lavish spending at Goodison has at least bought the experience to make a difference in matches as mundane as this. “It might have been different if we had done better with the final pass in the final third,” the Newcastle manager said. “In this kind of game when they are very physical and the referee allows them to do these things, and they are at home and have quality, that is an advantage.”

Unsurprisingly, Allardyce took an opposing view, suggesting Everton had been “excellent” for 75 minutes and lost their way only when Morgan Schneiderlin departed injured. Schneiderlin did impress, earning a rousing ovation from fans who had booed him on to the pitch a few months ago, but there was nothing excellent about this display beyond Walcott’s winner.

Allardyce had called for clarity over his long-term position before a game attended by Everton’s major shareholder, Farhad Moshiri. A glance to his left before the kick-off will have given the Everton manager a reminder of the clarification many supporters are hoping for. “Our survey says … Get out of our club” read a banner draped over the upper Gwladys Street stand. Anti-Allardyce sentiment had been reserved for Everton’s away matches, unsurprisingly given the contrast in results on the road and at Goodison, but the recent PR fiasco of asking fans to rate an unpopular manager on a scale of zero to 10 presented an opportunity that was not missed at home. A solid but unspectacular performance did little to appease the restless natives.

“The controversy was caused by an error from one of our employees who recognises it wasn’t the right thing to do,” said Allardyce on what was a wide-ranging survey. “As a manager you have to deal with it and move on. The players did the talking tonight by winning and moving us up to eighth. Let’s hope we finish the season as strong as we can.”

Newcastle arrived free of relegation concern after four successive wins and with Jonjo Shelvey seeking to press his claims for a World Cup call from the England manager Gareth Southgate. He was unable to do so as Schneiderlin and Idrissa Gueye controlled the midfield contest while a lack of composure with the final ball cost Newcastle several promising openings.

The visitors should have punished a miscued clearance from Jordan Pickford that invited Ayoze Pérez the freedom to play the fit-again Islam Slimani through on goal. Pérez badly overhit his pass, however, and the Everton goalkeeper was spared. Pickford was jeered throughout by the Newcastle support who have not forgotten nor forgiven the former Sunderland keeper for tweeting “Get the rave on” when his rivals were relegated in 2016. He responded with a “shush” gesture in the final seconds.

Walcott made an encouraging start to his Everton career but had gone nine games without a goal, and several anonymous performances, when he enlivened the match with a smartly taken breakthrough. Yannick Bolasie was the provider, driving down the right and using Coleman’s overlapping run to create space for a dangerous cross to the back post. The ball rebounded into Walcott’s path via the unwitting DeAndre Yedlin and the winger took an assured touch before driving high into Martin Dubravka’s goal.

Benítez, in his 100th game in charge of Newcastle, reacted by replacing Slimani with Gayle and the substitute should have equalised with his first touch. Shelvey’s corner was flicked on by Jamaal Lascelles to the striker, who had space inside the six-yard area, but his first-time shot sailed over Pickford’s crossbar.

Pérez and Matt Ritchie also had opportunities before the crucial diving header from Coleman in stoppage time, with Gayle poised to convert, secured an important win for Allardyce.