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A Luke Amos striker two minutes from time ended Wayne Rooney’s valiant attempts to keep the crisis club in the second tier.
Derby, who suffered a 21-point deduction due to entering administration and breaches of EFL financial rules, had their fate sealed when Reading grabbed a last-minute equaliser to draw 4-4 against Swansea.
Rooney told Sky Sports: "I’ve never seen a team relegated and the crowd react like they did today.
"You can see what it means to the fans. This is a special club and I want to be the one to bring the happy days back."
Reading fought back in sensational style after trailing Swansea 4-1 with half an hour of their game remaining.
Lucas Joao dispatched a third-minute penalty for the Royals, but Hannes Wolf quickly equalised with a superb curler into the top corner.
A Joel Piroe double, including Swansea’s first penalty of the season, and a brilliant Michael Obafemi effort put the visitors in control.
But Tom Ince gave Reading hope and Joao scrambled home before Tom McIntyre equalised in the fifth minute of stoppage time.
Peterborough kept their survival hopes alive with a 2-0 win at bottom club Barnsley, who have played one game fewer than Derby.
Goals from Jack Marriott and Frankie Kent moved Posh to within six points of Reading with three games remaining.
Bournemouth boosted their automatic promotion hopes with a 3-0 win at Coventry.
Jamal Lowe headed the Cherries into an early lead, and Dominic Solanke scored either side of the break to take his tally for the season to 27.
Huddersfield remain four points behind Bournemouth after winning 2-0 at Middlesbrough.
Former Boro striker Jordan Rhodes marked his return to the Riverside with an assist and a goal as the in-form Terriers made it 10 points from four games.
Rhodes set up Naby Sarr’s close-range header four minutes before the break before firing home only his second of the season on the hour.
Boro, who slipped down to ninth, are now without a win in four matches and in real danger of missing out on the play-offs.
Luton stay fourth after the Hatters’ Welsh boss Nathan Jones enjoyed a happy return to south Wales.
Harry Cornick’s 71st-minute header gave Luton victory on a day when they suffered potentially costly injuries to goalkeeper James Shea, James Bree and Fred Onyedinma.
Millwall stayed in the play-off hunt by beating Hull 2-1 at the Den.
A fortunate ricochet off Scott Malone put them ahead just after the interval, and Tom Bradshaw quickly added another as the Lions made it six wins from eight games.
Tom Eaves claimed a late consolation for the Tigers, but Millwall climb into seventh spot after Blackburn suffered a 1-0 home defeat to Stoke.
Jacob Brown’s fourth-minute strike for the Potters proved decisive at Ewood Park.
Blackpool thrashed Birmingham 6-1 as Jake Beesley marked his first start since his January move from Rochdale with a brace.
CJ Hamilton, Kenny Dougall, Jerry Yates (pen) and Callum Connolly were also on target for the Seasiders, with Ivan Sunjic providing scant consolation for Birmingham.
Additional reporting from PA