Reading’s recovery from 4-1 down to draw 4-4 at home to Swansea sealed Derby’s fate and left Barnsley and Peterbrough also on the verge of going down.
Derby delayed Fulham’s promotion party with a stunning 2-1 win over the league leaders on Friday, but needed a miracle to haul themselves out of a dire situation caused by financial problems.
The club remain in administration, although US businessman Chris Kirchner has been named as the preferred bidder ahead of a potential takeover.
Rooney’s men would be sat comfortably in mid-table without the points deduction for entering administration and breaching financial sustainability rules in previous seasons.
Luke Amos’ late goal secured a vital three points for QPR’s bid to climb into the playoff places and left Derby 10 points off safety with just three games to play.
Peterbrough stayed alive with a 2-0 win at bottom-of-the-table Barnsley, but are seven points adrift of Reading.
The Royals produced a remarkable fightback in the game of the day as eight goals were shared with Swansea with Tom McIntyre snatching a point deep into stoppage time.
At the other end of the table, Bournemouth have a four-point cushion over third-placed Huddersfield and two games in hand after a convincing 3-0 win at Coventry.
Dominic Solanke struck twice after Jamal Lowe had opened the scoring to move Scott Parker’s men to the brink of promotion.
Fulham, who are in action on Tuesday at home to Preston, could be promoted later on Monday should Nottingham Forest lose to West Brom.
Huddersfield all but secured their place in the playoffs as goals from Naby Sarr and Jordan Rhodes earned a 2-0 win at Middlesbrough.
Fourth-placed Luton are also in contention for a third promotion in five years as they won 1-0 at Cardiff.
Millwall were the big winners of those hoping to break into the top six as they beat Hull 2-1 to move level on points with Sheffield United, who travel to Bristol City later on Monday.