After being fouled by Paul Coutts 25 yards out, Iceland Under-21 international Sigurdsson calmly stepped forward to send a right-footed effort soaring past Joe Lewis and into the top corner of the net on the half-hour.
It was Sigurdsson's first Reading goal and Church came up with his own debut strike three minutes before the break.
This time Sigurdsson was the provider, lifting over a free-kick that the unmarked Wales international Church had all the time in the world to glance past a helpless Lewis.
Apart from an early opening for Boyd when Adam Federici saved easily, the nearest Posh came to what would then have been a leveller was a looping header by Chris Whelpdale that Shaun Cummings booted off the line as it looked to be dropping into the net.
Darren Ferguson shook things up at half-time, replacing Whelpdale and Toumani Diagouraga with Dean Keates and Lee Frecklington and, with Boyd seeing a lot more of the ball, Posh looked a different side, taking the game by the scruff of its neck and hauling themselves level with two goals in six minutes.
The first was a 48th-minute header by Craig Mackail-Smith from a Coutts corner before Aaron McLean latched on to a Boyd pass with such ferocity that Federici could only help the ball into the net. Federici also produced notable saves from Mackail-Smith and Frecklington as Posh stormed forward.
Mackail-Smith looked set to edge Posh in front on 70 minutes only to see his low angled drive turned against a post by Federici. But even the ever-agile Australia international couldn't stop Boyd's classy decider.