After all the headlines – worst Premier League start in history, worst top-flight start in Europe this season, "a disaster" according to the QPR board – Harry Redknapp was the very picture of nonchalance when he appeared for his post-match press conference. "Whose is that tea?" were his precise words, before slugging back a sip with: "Oh, cheers, thank you." But even the maestro of man management – who had his players in for an X Factor-style sing off to boost morale earlier in the week – could not entirely hide his pleasure at a potential season-changing three points.

"Yeah we deserved it," he purred, "we were the better team. It would have been a travesty if we'd conceded another goal in that last hectic couple of minutes ... psychologically the players must have been feeling: 'Oh my god,' when they got their goal, 'is an equaliser going to come here?' – you know? It was very difficult for me watching those last four minutes. But the players hung in there and we got what we deserved."

They certainly did. Fulham, seemingly jaded from a rare league win after turning the game around against Newcastle on Monday night, were lacklustre. So when Adel Taarabt, that capricious magician, put two past the visitors in the second half, there was a sense that Martin Jol's side would struggle to respond. Redknapp eulogised over the Moroccan star, "fantastic ability, amazing today", crediting Taarabt's performance to a reshuffle in the team formation.

"I decided I had to get him in a position where he wants to play," said Redknapp . "He's been playing out on the left, but today I put him in the hole off the front man, tried to get him between the lines, between their midfield and their back four, pop up in them positions, play little balls in them holes to him – and every time we got him on the ball they were in trouble."

It was indeed Taarabt who sparked the game into life, after a first half in which a sole goalscoring opportunity – a back-flick from Djibril Cissé to Jamie Mackie – constituted the half-time highlights package.

There had been tangible energy and drive from the QPR players from the outset, but as the clock ticked on, and they failed to convert their chances, self-doubt began to creep in, accompanied by loud choruses of "Stand up if you've won a game" from the away fans, to which there was no riposte.

The opening minutes of the second half snoozed along, with Fulham seemingly happy to coast, but all credit to Taarabt, he had other ideas. The 23-year-old winger popped up with a sensational strike – albeit  with a deflection off Brede Hangeland – that proved the game changer.

Suddenly QPR had their mojo back. Minutes later, Cissé almost doubled the lead, curving the ball just inches wide of the far post, before sinking to his knees and roaring angrily at the football gods lurking in the night sky. He need not have worried, though, for Taarabt had inspiration enough for a second goal, running almost the length of the pitch, to double QPR's lead.

Fulham halved the deficit after substitute Mladen Petric sent a looping ball towards goal – which took a deflection off Alejandro Faurlín – to give Fulham hope, and, in the dying minutes of the game, the tempo suddenly became frantic. Mark Schwarzer scooped a fantastic diving header from Cissé out of the goalmouth, while the home fans could hardly bear to watch as Fulham were given a free kick on the edge of the area.

At the finale, Jol was left feeling deflated. Unimpressed with the suggestion that QPR simply worked harder for it, the Fulham manager insisted his side should have more quality than simply being undone by the opposition's legwork. "We couldn't do the simple things, we couldn't play in a flow. I want them to play in a flow, with little combinations. Maybe Berbatov [did it] in spells, but he can't do it on his own. I wanted to give 10 of the 11 players who did it last week [the opportunity] to do it again, but it was not there."

For QPR, a run of four games unbeaten – and the club finally off the bottom of the table – signals a chance of a renaissance. But success may depend on what happens in the January transfer window, while losing Taarabt to the Africa Cup of Nations adds more complications.