Harry Redknapp's team showed their spirit and, in a wacky game of contrasting halves, they missed a penalty and nearly completed an outlandish comeback against a Fulham side that finished with 10 men after the harsh dismissal of Steve Sidwell.
But the blood and thunder could not mask the fundamental truth. Rangers really needed to win, yet they defended like schoolboys to leave themselves with too much to do.
Redknapp lamented a "disastrous" first half, which was scarred by "the worst goals I've ever seen in my life" and in the roll-call of shame, one man stood head and shoulders above the rest.
At 6ft 5in Christopher Samba has the capacity to do so but his performance was a personal nightmare that made a mockery of his £12.5m January transfer fee and the notion that he could be the club's survival talisman.
Redknapp even suggested that Samba had taken it upon himself to go up front after Sidwell's 78th-minute red card for a lunge at Armand Traoré, even though he wanted intelligent probing to expose the 10 men rather than high balls to the big lad. It must be said that Redknapp tied himself in knots on this point and was not entirely clear as the frustration of yet more squandered points bit hard.
At full-time Redknapp shook hands with his counterpart, Martin Jol, before making his way alone to the tunnel in the corner of Craven Cottage. He has 19 points from his 18 matches at Rangers but the club remain seven adrift of safety and have only seven matches to play. No team in Premier League history has escaped from such a position.
"We murdered them in the second half," Redknapp said, and there was a barnstorming quality about the Rangers revival, which had been ignited at the end of the first half when Giorgos Karagounis's loose back-pass led to Adel Taarabt beating Mark Schwarzer from distance.
Taarabt tricked Karagounis into nibbling at his ankles after the interval only for Loïc Rémy to telegraph his intentions from the spot and Schwarzer to read them and save. Yet Rémy hit back with a brilliant finish from Stéphane Mbia's pass and the visitors created a clutch of presentable chances, with Rémy blowing the best of them after he had beaten Brede Hangeland. Dimitar Berbatov called Fulham's defending "childish".
But Rangers' had been some way worse and Samba's catalogue of errors proved impossible to salvage. The first aberration had him losing his bearings and hacking down Ashkan Dejagah for a penalty that Berbatov tucked away without missing a heartbeat.
The second, though, was the most grisly. Samba dwelt on the ball as the last man when under pressure from Damien Duff and prodded the ball at Berbatov who eased into space to beat Julio César. "You can see which players are nervous and you look to push and press with them, which was the case with the second goal," Berbatov said.
"He is a clever guy, Berbatov," Redknapp said, sarcastically.
Fulham could have been further in front by then. Duff drew an early save from Julio César while Hangeland fluffed a free header. Berbatov dazzled in front of the TV cameras, drawing the breath when he beat Traoré with one touch from a high ball on the byline and Fulham's comfort in possession was indictment enough of Rangers' defending.
The third goal came when Hangeland's back-heel exposed Samba in embarrassing fashion and John Arne Riise's driven cross hit Clint Hill and flew home.
Samba tweeted a grovelling apology to Rangers' fans afterwards. "I can't say sorry enough," he said, and there was the accompanying promise to fight on.
But as Fulham embraced the near certainty of safety, the outlook was rather more grim for their neighbours.
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