Two goals from Adam Le Fondre earned Reading their first Premier League victory of the season, although Brian McDermott's side had to ride their luck during a dreadful first-half display and recover from a one-goal deficit.
The Everton manager, David Moyes, said: "I'm probably as pissed off as I've ever been" after a surprising turnaround. Le Fondre had not started a game for the Royals since their defeat by West Bromwich in September, but a second-half header and a winner from the penalty spot overturned Steven Naismith's opening goal to move Reading out of the bottom three.
McDermott said: "Adam's not played for a little while. It's a great header and then the man to take a penalty for your life is Adam Le Fondre. It's a relief and I'm so pleased for the players. That's been coming for some time."
Only 10 minutes had passed when Naismith gave Everton the lead. Atrocious defending by Reading resulted in a catalogue of errors in their penalty area, as an aimless hoof high into the air left the flummoxed centre-halves, Sean Morrison and Kaspars Gorkss, unable to clear their lines. Marouane Fellaini got between the pair and, when the ball ricocheted off the Belgian, Naismith gratefully poked in from close range.
Le Fondre had a chance to equalise when Tim Howard made a mess of a clearance, but the striker sliced wide after rounding the keeper. That was as good as it got for Reading in the first half. Quite how they escaped the opening 45 minutes without sustaining further damage was credit to Adam Federici, Everton's profligacy in front of goal and the referee, Martin Atkinson.
Steven Pienaar fired wide after Chris Gunter was caught in possession, before Thomas Hitzlsperger, making his first start for the club, and Leon Osman had efforts well saved. Everton should have had a penalty in the closing stages of the half. Nikica Jelavic's rasping drive from the edge of the area was on target before it clearly hit the arm of Morrison, but Atkinson gave a corner.
"I'm not angry with the referee. He should have given a penalty kick in the first half – it's hit his hand, it's going in and he doesn't give it," said Moyes. "I'm more angry with my team because we should have scored and it's down to us to do it. We didn't punish them, we left the door slightly ajar for them to come in and they did." Moyes said Everton "missed the leadership" of Phil Neville, who underwent knee surgery on Friday and will be out for six to eight weeks.
Reading equalised six minutes into the second half, Le Fondre leaping high and heading Nicky Shorey's free-kick into the top corner, before Seamus Coleman went through the back of the former Rotherham forward to concede a 79th-minute penalty. Le Fondre took his chance from the spot and, while Fellaini headed against the post at the other end, Reading were not to be denied.
McDermott said: "In any sport what you need to do is stay in the game. It is 100% about the group. The fans were fantastic, it's a good time to be a Reading supporter."