The home side had not conceded a goal for 405 minutes when Kevin Doyle fired the visitors ahead with a low 14th-minute shot in today's Coca-Cola Championship match.
But a minute later Noel Hunt netted from a similar position on the right side of the penalty area and from then on Coppell's men coasted to victory.
Doyle grabbed his second soon after the break and Kalifa Cisse made it 4-0 with a breathtaking 54th-minute strike, before Stern John grabbed an injury-time consolation.
A delighted Coppell said: "One of my favourite sayings is that when you work hard in football rewards don't come in equal instalments.
"We were by far the better side in our previous game at Burnley and came away with nothing. I am a firm believer that if you keep producing good performances results will come.
"Winning 3-0 at Wolves this season was a great achievement and this display was comparable.
"We felt we were going to give someone a hiding. Now we have to become more consistent because we have let ourselves down on occasions."
City boss Gary Johnson admitted his side had been outplayed in all departments.
He explained: "Reading were very good and we were extremely weak defensively.
"It was like a knife through butter at times and we have a lot of hard work ahead next week.
"Every player, apart from Stern John, had an off-day. We were not angry or committed enough and that has to change before we go to Southampton next weekend.
"You have to give Reading credit and they looked a very effective outfit. At our best we would have given them a game, but we were a long way of it."
Marcus Hahnemann had to make a superb flying save to keep out a John header on 36 minutes with the score at 2-0.
But Reading could have had more goals themselves and were always a yard sharper to the ball, with Doyle and Hunt working tirelessly up front.
Doyle's first away goal of the season came from a through-ball by Liam Rosenior, making a successful return to his former club.
Jimmy Kebe put Hunt in for the second goal and was also involved in the third goal on 47 minutes when his low cross led to a Doyle tap-in at the far post.
Cisse struck the goal of the game as he connected sweetly from 20 yards and bent the ball around Adriano Basso's dive.
Coppell could afford to withdraw both his impressive front men as City never remotely suggested a recovery.
John's volleyed goal at the death was well deserved. The Southampton loanee was his side's only threat on an afternoon they will want to forget.