Joyous Queens Park Rangers earned their first Premier League win since 1996 as Tommy Smith punished wasteful Everton.
In their first match under new owner Tony Fernandes, the visitors led on 31 minutes when Smith curled in low after Phil Jagielka had lost possession.
Leighton Baines had earlier hit the crossbar with a free-kick.
Tim Cahill headed the best chance wide from three yards out as cash-strapped Everton fell to a first home league defeat of 2011.
Despite the financial pressures on them, long-serving Toffees boss
David Moyes insists
he can keep hold of his most established players.
'Amazing result' for Warnock
But 17-year-old Ross Barkley started, and shone, in midfield while playmaker Mikel Arteta and Maroune Felliani sat on the bench.
Playing their first match of the season after the scheduled opener at Tottenham was postponed because of the recent riots, Everton began with enterprising purpose.
Jermaine Beckford, spearheading the attack on his own, could not connect with a scissors kick while Cahill - bravely diving low - was inches away from putting his head on a wicked Baines delivery.
Following inventive jinking work from Barkley, Baines then curled an almost perfect free-kick over the wall, but his effort crashed down off the bar.
As Shaun Derry battled hard for the visitors, QPR - who had been hit by a virus in the camp - snatched the lead.
Jagielka gave the ball away uncharacteristically, allowing Akos Buzsaky to feeding a pass to Smith in the box, and the 31-year-old took a touch and spun to curl the ball instinctively beyond Tim Howard into the bottom corner.
Sliding Jagielka was a second too late to atone for his error.
Unmarked, Cahill missed Everton's best chance - a virtual open net - after Beckford had swung over a threatening cross to the back post.
Rangers were caught dozing seconds after the break but Jack Rodwell lifted a weak shot into Kenny's hands when the clear chance demanding a powerful, low strike.
Everton lacked quality - Moyes
Arteta replaced him soon after, just before striker Patrick Agyemang was stretchered off with a leg injury, and Everton predictably pressed with increasing desperation.
But, typifying the work ethic, Derry made a superb sliding block on Osman after he shaped to shoot following a surging run.
Fellaini came on and immediately set up Cahill but he dithered too long and his shot, from too wide an angle, was easily batted away.
Everton manager David Moyes:
"Ross [Barkley] should be proud of the way he played today, the way he took responsibility on the ball. He was terrific. He was the one who looked likeliest to craft a chance today.
"Probably not with the way we played, but I don't think we deserved to lose it either. When we created we didn't take the chances we had. You always felt a sense of anxiety that we were chasing the game. We just didn't have the quality on the right areas to make the difference. You need the players to help you finish your good moves off.
"I don't think I can do anything in the transfer window. I'm definitely short of forwards and wide players. But we were last year as well.
QPR manager Neil Warnock:
"It's an amazing result. Yesterday we lost three players with a virus. One of them, DJ Campbell, collapsed. But everybody played as a team.
"I felt we deserved it in the end. We've just got to get on with it after last week. It's a fabulous league, I love it. We've got to enjoy it.
"I've never been busier. We're going to try to bring four or five players in who can help us. I'm really looking forward to it, to really competing. I'd be very surprised if I don't get the players in."
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