Jimmy Kebe also netted as the Royals jumped up to 18th in the table and pushed the Eagles nearer to the drop zone.
Palace have lost their last two matches at Selhurst Park and Sean Scannell's first goal in 13 months will not have lifted the gloom as they are only outside the bottom three on goal difference.
Palace had started brightly and Darren Ambrose's right-foot volley from the edge of the box after five minutes forced Adam Federici into a fine one-handed save.
Calvin Andrew should have done better from Danny Butterfield's cross on 17 minutes, but his header cleared the bar as the home team made the early running.
But they were made to pay for their wastefulness when Jobi McAnuff's cross to the back post was acrobatically volleyed by Church past keeper Julian Speroni in the 23rd minute.
The Wales international squandered a great opportunity just before the break when Brian Howard's pass sent him clean through, his touch let him down at the key moment and Speroni was able to make a block.
Ambrose's fierce 30-yard shot forced Federici into another excellent stop in the opening moments of the second half, but Reading made it 2-0 on 47 minutes.
Brynjar Gunnarsson's right-wing cross was flicked into Kebe's path by Palace midfielder Nick Carle and he produced a composed finish from eight yards.
Church's shot clipped the post in the 51st minute before Scannell boosted hopes of an Eagles comeback as he headed in Ambrose's corner.
Butterfield's 25-yard strike just cleared the bar as the home side desperately sought an equaliser, but Church killed off any uncertainty over the outcome with ten minutes to go, guiding the ball home after Matt Mills' low cross.
Speroni made saves from Gylfi Sigurdsson and Kebe to prevent Reading from winning by an even greater margin.