Everton 1-0 Derby: Everton clung onto their dream of Champions League football next season but this was a dire performance against the already relegated Midlanders.
Derby have succumbed to the quickest relegation from the Premier League and this 27th game without a league victory is also a new record for the competition. But they are going down with pride and they worked hard to give boss Paul Jewell hope for the future.
It took a second-half goal from midfielder Osman, his seventh of the campaign, to put the anguished Toffees' fans out of their misery.
Everton have now cut fourth-placed Liverpool's lead over them to three points, but for long spells it looked as if the Goodison Park club had already thrown in the towel.
They were dreadful in the first period and only marginally better after the break.
Taking them to Marbella this week for warm-weather training may not have been boss David Moyes' best move, because his team looked as if they were dreaming of their sunshine break for long spells.
Everton lost Tony Hibbert (hip) and Steven Pienaar (knee) ahead of the match, while Phil Jagielka was rested to the bench from the team that lost at Liverpool last weekend.
It meant that Leighton Baines returned to defence, Manuel Fernandes to midfield and Andrew Johnson up front. Victor Anichebe, who had spent the early part of the week in hospital after being taken ill with a virus, was on the bench.
Derby, who had scored more than twice in a league match for only the third time this season in drawing 2-2 with Fulham last time out, kept an unchanged team.
And Derby surprised Everton with their desire to go forward, with Tim Howard only able to palm the ball out from an 18-yarder from Mile Sterjovski after six minutes.
Everton may have been disheartened by Liverpool's draw at Arsenal the previous day, a result they were not expecting in the race with their neighbours for fourth spot.
They were disjointed and certainly in the opening period they lacked the drive and spirit normally so evident in Moyes' teams.
Mikel Arteta's run from midfield and chip over Roy Carroll's bar was the best they could do early on.
But Ayegbeni Yakubu should have grabbed the lead after 17 minutes, scooping a shot over the bar from four yards when Baines' cross from the left reached him unmarked on the far post.
Carroll then saved low down from Fernandes, but there was precious little spark or urgency from either side.
Andy Todd was booked for a foul on Baines, at that stage the only tackle with the slightest venom in it. Three minutes later Phil Neville was cautioned for a body-check on Robbie Savage.
Hossam Ghaly wasted a couple of half-chances that could have been decent openings with greater control but it was Everton's general lethargy that gave Derby hope.
When Arteta lifted a free-kick from the edge of the box high over Carroll's bar, it underlined the abject nature of the match.
Everton clearly had a few home truths from Moyes at the break and were sharper and quicker about the pitch. Carroll saved well from a fierce angled drive from Fernandes but Yakubu wasted the follow-up effort.
But after 56 minutes Everton finally scored, Derby standing and watching as Fernandes fired a 30-yard pass from the left into the path of Leon Osman running from deep into a huge space in the visitors' back-line. Osman took one touch and lashed his shot past an exposed Carroll and all Derby's positive work beforehand looked wasted.
Carroll then saved well from two other Osman efforts. But Emanuel Villa should have equalised after 64 minutes when Todd's through ball sent him clear but the weak effort was blocked by Howard's out-stretched left leg.
Ghaly was booked for a foul on Johnson before Everton sent on Anichebe for Yakubu after 73 minutes. Four minutes later Jagielka replaced Fernandes.
Derby kept working, and twice Kenny Miller saw long-range efforts go wide.
Savage was booked after 85 minutes for a foul on Arteta but it was Everton defending in the closing minutes to keep out Derby's attempts to equalise.
Everton sent on Nuno Valente for Arteta in injury-time, Derby by this time having won a string of corners, with 'keeper Carroll staying up for all of them, in a desperate attempt to claim a point.