Marouane Fellaini headed the Toffees ahead with his 12th goal of the season late in an evenly-fought first-half, in which Reading hit the woodwork, and the Merseysiders eased to victory after the break.
Steven Pienaar, with a stunning long-range strike, and Kevin Mirallas made sure of the three Barclays Premier League points before Hal Robson-Kanu grabbed a consolation.
Defeat left Reading in the bottom three and in the thick of a battle for survival while Everton, after last week’s disappointing loss at Norwich, could still entertain hopes of finishing in the top four.
There was an element of the unknown about both sides as goalkeepers Tim Howard and Adam Federici were ruled out through injury. Jan Mucha came in for Everton, ending Tim Howard’s run of 210 consecutive league appearances, while Stuart Taylor made his Reading debut and a first Premier League outing in five years.
Nikica Jelavic spurned an opportunity to test Taylor when he headed well wide inside the first minute but it signalled the start of an entertaining opening period in which both sides had good spells.
Everton were forced to make an early change, however, after Phil Jagielka failed to run off the effects of a bad challenge from Adam Le Fondre, for which he was booked, in the second minute. John Heitinga replaced the centre-back in a straight swap.
The hosts had the better early openings as Pienaar had a shot blocked by Stephen Kelly and Fellaini shot wide. Jelavic headed straight at Taylor from a Mirallas cross but Reading began to threaten on the counter-attack.
Jimmy Kebe stole possession from Leon Osman and charged upfield only to shoot wide and Le Fondre won a free-kick on the edge of the box. Ian Harte hit the target from the set-piece but Mucha saved well.
Kebe went through on goal but was unable to get round Mucha and pulled up injured seconds later. He tried to run off the blow on the sidelines but Reading also had to turn to the bench early and Wales international Robson-Kanu was sent on.
Reading kept up the pressure and Everton were relieved when an unmarked Le Fondre screwed a shot against the top of the post from a corner when he should have found the target. Leighton Baines broke down the left as the Toffees responded but Adrian Mariappa blocked Pienaar’s shot.
Taylor then proved his worth with good saves in quick succession from Jelavic and Mirallas but Reading cracked three minutes before the interval. Seamus Coleman found space on the right and delivered a perfect cross for Fellaini to rise and head home with trademark power from six yards.
Fellaini ended the half by attempting to score a second from an outrageous angle but Taylor was alert and palmed over. Taylor was in action again early in the second period as he came out to block an attempt by Mirallas.
Reading then somehow managed to survive a goalmouth scramble in which Jelavic and Fellaini both had opportunities at close range. Jelavic also went down under a challenge from Kelly but the referee was unimpressed.
Reading had their own penalty appeal moments later as they claimed handball against Sylvain Distin but again nothing was given. Everton doubled their advantage just before the hour when Pienaar took a pass from Fellaini and set off on a run towards goal. The South African cut inside two defenders on the edge of the box and unleashed a ferocious strike into the top corner which gave Taylor no chance.
Everton were not finished there and Fellaini almost turned in a Mirallas drive at the far post. The third goal was not long in coming and Mirallas showed great composure to clip past Taylor after exchanging passes with Pienaar to race through on goal.
The hosts refused to ease off as Darron Gibson flashed a long-range effort narrowly wide and Taylor produced a good save to deny Mirallas. To their credit, Reading battled on, even if only to reduce the damage to their goal difference column.
Mucha made a good save from Jobi McAnuff and the visitors did pull one back six minutes from time as Harte crossed from the left and an unmarked Robson-Kanu headed home with conviction.
Everton substitute Victor Anichebe went close to restoring a three-goal advantage when he chipped Taylor but Harte volleyed clear off the line.