Last year's League One champions Leicester move into the play-off places with this stolen win while the Royals remain in the relegation places and without a home win in the Championship for nine months.
In Rodgers' defence, of the XI who started Reading's last home win over Wolves way back on January 27, only Adam Federici and Alex Pearce started for this, their 16th attempt at victory in front of their own fans since.
Reading have lost Kevin Doyle, Stephen Hunt, Leroy Lita, Andre Bikey and James Harper among others since failing to win promotion last May and look desperately short of a cutting edge.
Church, Jobi McAnuff and Grzegorz Rasiak all had presentable chances in a bright opening before Reading should have taken the lead in the 25th minute.
Church released McAnuff and after outpacing the Leicester defence the winger hit a shot down into the turf which bounced past goalkeeper Chris Weale and into the far post.
McAnuff reacted well to hit the rebound toward goal but left-back Ryan McGivern made a fine block to keep the ball out.
The officials somehow awarded a goal-kick to the fury of the home crowd and Paul Gallagher came close to increasing the sense of injustice when he curled a shot onto the roof of the net after a rare Leicester break.
Church then wasted the best chance of the half when Rasiak's flick sent him in on goal but the Wales international dragged his shot wide of Weale's post.
Church was denied by an excellent save from Weale moments later after an elaborate corner routine fell to him inside the area and had time for another shot off target before half-time.
Reading had dominated for a spell of 30 minutes but predictably it was Leicester who forged ahead in the final minute of the half.
Matt Oakley delivered a corner from the right and Waghorn got ahead of Gylfi Sigurdsson to flick a header over Federici and into the net.
Church missed another golden chance five minutes after the restart when he scuffed into the side-netting but Matty Fryatt could have doubled the lead at the other end when he beat the offside trap but could not beat Federici.
Reading's lack of a predatory goalscorer was again highlighted when McAnuff and then Ryan Bertrand cut balls across the face of a vacant goal as the crowd began to turn on Rodgers.
Substitute Jimmy Kebe then squared for Rasiak to spurn a final opportunity as Leicester held on for the win.