The visitors looked to be in control with two goals from Romelu Lukaku but Jimmy Kebe pulled one back before Le Fondre's penalty and Pogrebnyak's goal earned them all three points.
Reading goalkeeper Adam Federici denied James Morrison, who had been picked out by Jerome Thomas.
West Brom then took the lead when Lukaku released Morrison down the left and then received the return ball to beat Federici from six yards.
Chris Gunter worked some space down the same flank he floated a cross in for Jobi McAnuff but the Reading captain could not generate any power and Ben Foster claimed his soft header.
Reading were fortunate not to go further behind immediately after the restart when Ian Harte conceded possession and Lukaku almost doubled his tally.
Chris Brunt preserved West Brom's lead with a last-gasp block to deny Garath McCleary after Foster had missed Kebe's cross.
Lukaku had one strike chalked off for offside before he hit the post with a glancing header. He then rattled the crossbar with a thundering left-foot strike before finally hitting the target again, drilling a low shot past Federici. Morrison fed Lukaku and he stepped inside Adrian Mariappa and beat Federici at his near post.
With 10 minutes left Kebe snuck in at the back post to meet McCleary's cross and beat Foster with a header. Kebe was then clattered by Jonas Olsson on the edge of the West Brom box and Le Fondre tucked the penalty away calmly to Foster's left.
An incredible comeback was completed when Harte launched a free-kick into the box, Alex Pearce knocked it down and Pogrebnyak bundled the ball past Foster.