The Royals laid siege to the Posh goal right from the start and scored four times in the first-half, although it could easily have been many more.
Reading's first came after just two minutes. Skipper Brian Howard was fouled by Ryan Bennett and took the free kick, which was diverted for a corner. Howard took that as well and it was put into the Peterborough net by centre back Alex Pearce, whose header came of Peterborough's Gabriel Zakuani.
Referee Carl Boyeson angered Reading when Scott Griffiths appeared to send Sigurdsson tumbling in the penalty area, only to show Sigurdsson a yellow card for simulation.
Minutes later Reading were awarded a penalty when Ryan Bertrand was brought down by Craig Morgan. Sigurdsson stepped up to score his 17th goal of the season
Reading added their third in the 29th minute when Sigurdsson set McAnuff free and the winger hammered the ball across the face of the Peterborough goal and into the far corner.
Six minutes before the break Kebe had a glorious chance to add another for Reading after he was put clear by Jay Tabb and, with only Joe Lewis to beat, he delayed his shot, allowing the keeper to smother his effort.
The fourth Reading had been threatening came a minute before the break. Full-back Andy Griffin sent Kebe clear and this time he made no mistake, hammering the ball past Lewis.
Early in the second half Lee Frecklington briefly raised hopes of a consolation goal for Peterborough when he broke clear but shot tamely into the side netting.
It was Reading who scored again though. A clearance by Pearce was collected by Sigurdsson and his quick pass through the Peterborough defence sent Long clear to shoot past Lewis.
Then Long hit the Peterborough bar from point blank range, only for Sigurdsson to score from the rebound to complete a majestic afternoon in Berkshire.