Rangers, who were so outplayed in the first half it was embarrassing, would have snatched a draw in the second were it not for a missed penalty by Bradley Allen.
Instead they now have just a long struggle with relegation to contemplate. "It is a difficult time, I expect to get criticism," Ray Wilkins, the QPR manager, said. "But I draw a lot from the pride the players showed in the second half. I do not feel under pressure."
For Wilkins' former England colleague, Glenn Hoddle, there appear only good things ahead. His team have lost once in 14 games and they will travel to the winners of the delayed fourth-round tie between West Ham and Grimsby with confidence.
Allen's 70th-minute failure came three minutes after a stunning volley from 17-year-old Nigel Quashie had thrust Rangers back into a tie which had seemed beyond them. Chelsea, while fortunate to take a 17th-minute lead through Gavin Peacock, were well in control by the time Paul Furlong added a second in first-half injury time.
With Ruud Gullit at the hub of their sweet passing moves they had exposed the paucity of Rangers' resources. Gullit, taking a more dominant role in the absence of the suspended Dennis Wise, should have scored himself in both halves. After Jurgen Klinsmann last season maybe Gullit's Wembley progress will be this year's Cup cause celebre.
Peacock's goal, deflected off Andy Impey, followed a neat interchange involving Gullit and John Spencer. The Scot then showed acute awareness of space for the second, chipping Furlong clear with an overhead kick from Michael Duberry's long pass. Furlong had only scored once before this season - in the League defeat of QPR on this ground last month.
The second period began with Chelsea indulging in tricks and their supporters chanting "Ole". However, by the close they were whistling anxiously for the end.
Rangers, lifted by the crowd in this compact stadium, had gradually come into the game by the hour mark. Chelsea, having ignored a warning shot from Allen, paid for their lethargy with 23 minutes left. Ian Holloway's partially cleared corner reached Quashie, who thrashed it back in from 20 yards.
Then Trevor Sinclair's cross caused panic in Chelsea's area during which Kevin Hitchcock bundled over Mark Hateley. Allen stepped up, and dragged the spot-kick wide. "We do not have a penalty-taker - Bradley felt confident he would stick it in," Wilkins said.
In a frantic finish chances came and went at both ends, though none was as clear as the header Hateley missed from five yards in the third minute. But it was the memory of the penalty that lingered. "We would have won if it had gone in," Wilkins said ruefully.
Queen's Park Rangers (4-4-2): Sommer; Bardsley (Maddix, 11), McDonald, Yates, Challis; Impey, Quashie, Holloway, Sinclair; Allen, Hateley. Substitutes not used: Brazier, Gallen.
Chelsea (3-6-1): Hitchcock; Duberry, Lee, Clarke; Petrescu, Peacock, Gullit, Newton, Spencer, Phelan; Furlong. Substitutes not used: Johnsen, Morris, Kharin (gk).
Referee: P Durkin (Portland).
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