The Royals captain struck in the 26th minute as the Championship side edged a tense fifth-round tie at Goodison Park to reach the quarter-finals for a second successive year. Brian McDermott's side, who beat Liverpool en route to the last eight a year ago and overcame West Brom in the third round, will now play Manchester City or Aston Villa.
McDermott said: "You have to be disciplined when you come here - they passed it around for the first 20 minutes and did really well. But we did what we had to do and I thought we were deserved winners. It is a great night for the players."
He added: "I felt that if we set our team up in the right manner and went about business in the right way, I knew we had players who could make a difference.
Reading should have had a second when Jimmy Kebe broke clear but Tim Howard did well to deny the Mali international.
Everton finished strongly but Reading's second-choice goalkeeper Alex McCarthy, deputising for the injured Adam Federici, held firm and produced one fine save from a fierce Leon Osman volley.
McDermott added: "I thought we were excellent from start to finish. We had to hang in there at the end when Osman had the opportunity but Alex McCarthy made a match-winning save."
Defeat was yet another frustrating result in an inconsistent season for Everton.
Manager David Moyes had hoped his side's emotional victory over Chelsea in the fourth round could spark an upturn in fortunes but the players could not respond.
He said: "We didn't play well enough and we got what we deserved. We didn't have enough quality, enough craft or guile to break them down at the top end of the pitch."
Source: PA
Source: PA