Hal Robons-Kanu put the hosts in front after just eight minutes, but the lead lasted just five minutes after Anderson fired an excellent equaliser inside Adam Federici's near post.
A Wayne Rooney penalty put the Reds 2-1 up soon after, before Reading drew level through Adam Le Fondre and then regained the lead when Sean Morrison headed home from a corner.
Rooney made it 3-3 on the half-hour mark, before Robin van Persie netted the decisive strike four minutes later. The Dutchman should have been credited with another goal before the break when his close-range shot was cleared by Adrian Mariappa, but referee Mark Halsey and his assistants failed to spot that the ball was already over the line.
Click on the image above to view a gallery of photos from the Madejski Stadium.