Everton kept alive their flickering hopes of a fourth-place finish at Goodison Park yesterday, but it was a far from convincing performance that carried them past a Derby County team for whom unwanted records continue to tumble.

A 1-0 defeat extended Derby’s winless streak to 27 Barclays Premier League matches, eclipsing the previous worst set by Sunderland during their ill-fated 2005-06 campaign, but while Everton probably deserved their victory, Liverpool are unlikely to be concerned if their Merseyside rivals finish the season in this form.

Everton moved to within three points of Liverpool courtesy of Leon Osman’s seventh goal of the season, but against most other Premier League teams, David Moyes’s men might not have been so lucky.

Seldom have Everton played so poorly this season, although a first league win in four matches will boost confidence going into a run-in that, despite featuring three home matches, is tougher than Liverpool’s. “The result was all-important today,” Moyes said. “Results at this time of the year are not as easy to come by as some people think and that was the case today. Sometimes a result like this can be the thing that gives you the boost you need.”

Everton played in the first period, and for moments in the second, in the way Derby have for the vast majority of this season: fearful, lethargic and lackadaisical in possession. By contrast, relegation appears to have freed Paul Jewell’s team of their shackles.

Of course, however bad the opposition, there is always the chance of Derby shooting themselves in the foot with a customary lapse of concentration and such a moment occurred in the 56th minute. Osman drifted into the giant hole created by Darren Moore and Dean Leacock, the Derby central defenders, and was easily picked out by Manuel Fernandes before shooting beyond Roy Carroll.

Merseyside had played host to the Grand National over the weekend, but Osman was the only Everton player at the races. Not content with his goal, he forced two smart saves out of Carroll, but Everton’s lead remained fragile.

Emanuel Villa had given the home team a fright in the 64th minute when he beat the offside trap, but when one on one with Tim Howard, a cool head deserted him.

Yakubu Ayegbeni has been one of the bright sparks of Everton’s season, but he missed three inviting opportunities as the home side clung on to leave Derby frustrated at not having taken more from the match.

Everton (4-4-2): T Howard 6 – P Neville 6, J Yobo 6, J Lescott 6, L Baines 6 – M Arteta 5 (sub: N Valente, 90min), L Carsley 5, M Fernandes 6 (sub: P Jagielka, 77), L Osman 7 – A Johnson 5, Yakubu Ayegbeni 4 (sub: V Anichebe, 73). Substitutes not used: S Wessels, T Gravesen. Booked: Neville. Next: Birmingham (a).

Derby County (4-4-2): R Carroll 7 – A Todd 5, D Moore 4, D Leacock 4, E Lewis 5 – M Sterjovski 5 (sub: T Mears, 51 5), R Savage 6, H Ghaly 6, D Jones 5 – K Miller 6, E Villa 5. Substitutes not used: L Price, J McEveley, R Earnshaw, B Feilhaber. Booked: Todd, Ghaly, Savage. Next: Aston Villa (h).