All is not yet lost for Everton in their bid to overhaul Liverpool in the race for fourth place and Champions League football. Leon Osman's second-half goal gave them this thoroughly expected victory and secured a two-point weekend swing over their neighbours who had beaten them the previous Sunday.
The gap is back to three points and three of Everton's remaining five games are at home, although they will need to play better than this to take anything from Chelsea in the first of them.
Had they been facing anyone other than Derby County yesterday, they would have been in danger of another of their occasional surprise aberrations, which have cost them dear against Oldham Athletic and Fulham this season.
They emerged deservedly enough from a dip of three League games containing one goal and one point but their manager David Moyes was not in raptures. "Results at this time of year aren't as easily come by as people sometimes think," he said. "That was the case here. We didn't show a lot of energy and need to go again – that's the big thing – because we didn't play well."
Derby have been staring into the abyss for months. They were also peering through a snowstorm when a dreary deadlock was broken in the 56th minute.
Manuel Fernandes, who had swapped with Osman by going wide at the start of the second half, did what Derby hopelessly failed to do by spotting his colleague's fine run through the middle. With the considerable time and space he was afforded, Osman controlled and finished unerringly inside Roy Carroll's near post with his left foot, his spell of four and a half months without a Premier League goal over.
Fernandes and Osman did more than anyone to inject urgency after a first half that will be remembered only for an astonishing scoop over the bar from four yards by Yakubu from Leighton Baines' low centre. Fernandes had just seen a 25-yarder beaten out by Carroll, who would later deal similarly with efforts by Osman inside and outside the penalty area as Everton laboured to shake off their post-derby lethargy.
Derby, for the position they are in, performed respectably without ever threatening to avoid what now stands as an outright record of 27 Premier League matches without a victory. Mercifully near the end of a season of incessant depression, they attacked brightly at times and forced a flurry of corners in the dying minutes.
They also worked Tim Howard with long-range efforts by Mile Sterjovski and David Jones early in each half and went closer still midway through the second half when Joseph Yobo foolishly stepped out in search of an offside flag from Andy Todd's through-ball and left Howard, after a dummy by Kenny Miller, to save with his foot from the clean-through Emanuel Villa.
Relegated Derby remain five points adrift of avoiding the dishonour of becoming officially the worst side in Premier League history but, with the on-loan Hossam Ghaly impressing in midfield, they hinted at being a force in next season's Championship.
"I thought we deserved a point and passed it well between the two boxes," said Paul Jewell, whose Derby reign now adds up to five draws and 14 defeats from 19 league games. "It's easy to improve, though, when you're relegated. It's what happens next season that interests me more."
Goal: Osman (56) 1-0.
Everton (4-4-2): Howard; Neville, Yobo, Lescott, Baines; Arteta (Valente, 90), Carsley, Fernandes (Jagielka, 76), Osman; Yakubu (Anichebe, 74), Johnson. Substitutes not used: Wessels (gk), Gravesen.
Derby County (4-4-2): Carroll; Todd, Moore, Leacock, Lewis; Sterjovski (Mears, 50), Ghaly, Savage, Jones; Villa, Miller. Substitutes not used: Price (gk), McEveley, Earnshaw, Feilhaber.
Referee: A Marriner (West Midlands).
Booked: Everton Neville; Derby County Todd, Ghaly, Savage.
Man of the match: Osman.
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