David Moyes has become accustomed to fielding questions about Everton’s prospects of finishing fourth, but after watching his players overcome a stubborn Reading team on Saturday, the manager was asked whether catching Chelsea, in third, was realistic. “That’s a new one,” Moyes said, before warming to the idea of challenging a team who are in the title race.

It is a reflection of Moyes’s ambitions and rising expectations at the club that the manager could entertain such suggestions. Liverpool fans will snigger, but as Everton strive to finish above their Merseyside rivals and secure Champions League qualification for the second time in four seasons, supporters in the red corner may concede that the gap is closing – fast.

“We played them [Chelsea] a couple of weeks ago and we know what they have done,” Moyes, alluding to their Carling Cup semi-final defeat by Avram Grant’s team, said. “We have a bit to go before we get [to where Chelsea are], but the aim for me is to make that happen when I can.”

Given the level of competition, fourth place would be some achievement this season and as long as Everton are not driven to distraction in Europe – they travel to Bergen, in Norway, to play Brann in the first leg of their Uefa Cup last32 tie on Wednesday before the return match at Goodison Park eight days later – their prospects are favourable.

They will have to play better than they did against Reading, but Everton are becoming adept at winning when not at their best, a trait of all the top teams. It was by sheer persistence that they inflicted a record-equalling seventh straight defeat on Reading, whose prospects of staying in the division appear to be receding with every passing week.

Phil Jagielka’s first league goal for Everton settled a scrappy match that was hardly the advert for Premier League football that Richard Scudamore, the organisation’s chief executive, would have wanted as he attempts to sell the league around the world, but one that demonstrated all of the values that Moyes holds dear.

Having omitted Yakubu Ayegbeni, Everton’s leading scorer, from his squad as punishment for returning late from the African Cup of Nations, Moyes emphasised that “the performance” mattered to him as much as the points and expected an improvement from his team in the months ahead.

Given that perseverance was the theme of the day, it seemed fitting that Jagielka’s goal should decide a match that turned in Everton’s favour with the half-time introduction of the lively James Vaughan. Jagielka, the former Sheffield United player, had a difficult start to his Everton career but is starting to flourish. An hour had elapsed when he looped a header over Marcus Hahnemann, then, with six minutes to go, he denied Jimmy Kebe a goal with a terrific last-ditch block.

“You know what you are going to get with Everton, but they do it very well,” Steve Coppell, the Reading manager, said. “They don’t give much away. They are strong physically and mentally and that is important.”

Everton (4-4-1-1): T Howard 6 – P Neville 6, P Jagielka 8, J Yobo 7, J Lescott 6 – M Arteta 6, L Carsley 5, M Fernandes 5 (sub: J Vaughan, 46min 7), L Osman 5 – T Cahill 4 – A Johnson 4. Substitutes not used: S Wessels, A Hibbert, A van der Meyde, N Valente. Next: Manchester City (a).

Reading (4-4-2): M Hahnemann 6 – G Murty 6, I Sonko 6, K Cissé 6, N Shorey 5 – J Oster 5 (sub: J Kebe, 81), M Matejovsky 6, J Harper 5, S Hunt 5 – K Doyle 5, D Kitson 5 (sub: S Long, 75). Substitutes not used: A Federici, L Rosenior, U De La Cruz. Next: Manchester United (h).