After failing to make their first-half dominance count, the Toffees were made to rue their profligate finishing as an Adam Le Fondre double gave the hosts all three points
The Toffees dominated proceedings throughout the first half, opening the scoring after ten minutes through Steven Naismith, but failed to double their lead while they had two big penalty shouts turned down.
Adam Le Fondre pulled one back just after the break, however, and with the visitors going all out for the win the game became very open. Then, with about ten minutes remaining, Reading were awarded a penalty, after a foul on Le Fondre - the striker stepped up himself and tucked it away to hand his side their first victory of the season.
The hosts made two changes from the 0-0 with Norwich; Hal Robson-Kanu and Adam Le Fondre coming in for Garath McCleary and Noel Hunt. Meanwhile David Moyes also made a couple of replacements, bringing in Thomas Hitzlsperger and Naismith for Kevin Mirallas and Phil Neville.
The Toffees made the brighter start to the game, and should have taken the lead very early on. Adam Federici firstly saved superbly to deny Phil Jagielka, before Nikica Jelavic made a hash of a brilliant chance moments later, his effort from two yards out going over.
However Moyes' men didn't have to wait long for the breakthrough, and they didn't have to work that hard either - the Royals' defence absolutely gifting them the opening goal.
Chris Gunter failed to rid the danger when his sliced clearance went up high and into his own box, then a mix-up between Kaspars Gorkss and Sean Morrison firstly allowed Marouane Fellaini to win the ball, though the hosts then half-cleared the danger, only for Jelavic to get it back and cross for the arriving Naismith - finding Gorkss and his defensive colleagues asleep once more.
Although Reading had a brilliant chance to level straight away, Le Fondre beating Tim Howard to a loose ball but lifting the ball over the bar as he tried to evade the men on the line, the rest of the first-half pressure all came from the visiting side.
Steven Pienaar nearly doubled the score, but dragged his right-footed shot wide, before Everton saw the first of two penalty appeals turned away. Gorkss slid in recklessly from behind on Naismith, getting none of the ball, but the referee waved play on.
The visitors continued to create openings, Leon Osman seeing a one-on-one saved by Federici and Jagielka having a glancing header cleared off the line, while they were could have had another penalty when Jelavic's drive struck Morrison's hand, but for all their dominance the half ended 1-0.
After the break, however, Reading got themselves back into the game though Le Fondre. The forward rose the highest and got his head on the end of Nicky Shorey's dangerous free-kick, beating Howard with a thumping effort.
The game then become incredibly open. Hitzlsperger wasted a clear opening by allowing Morrison to get back and block his effort, before the Everton man was then disposed at the other end by Roberts, who played in Le Fondre only for the Royals' goalscorer to scuff it into Howard's arms.
As the clash became more stretched, Le Fondre looked to be in on goal after a quick counter-attack, however, Seamus Coleman came out of nowhere to disposes him with a fantastic, goal-saving tackle.
The defender soon turned from hero to zero, though, as he conceded a penalty for a clumsy challenge from behind on Le Fondre, bundling the forward to the ground. Reading's number nine took it himself, sending Howard the wrong way and giving his side the lead and their first three points of the campaign.