Williams produced a clinical finish in the 70th minute to earn Reading three points on their travels for the first time since they won at Norwich on November 29.
In the process he sent high-flying Wolves crashing to their first defeat in nine league matches.
Reading had made the perfect start to the match when Pogrebnyak gave them the lead after just 20 seconds.
Benik Afobe pegged them back with a 26th-minute equaliser as he scored his second goal for the club following last month’s £2million move from Arsenal before Williams earned Steve Clarke’s side a deserved win following an impressive second-half display.
Reading caught Wolves cold when they took the lead through Pogrebnyak’s second goal in two games to make it a miserable start for the home side’s debutant goalkeeper Tomasz Kuszczak.
A neat flick from Simon Cox dropped over the top of the flat-footed Wolves defence and Pogrebnyak flashed a right foot drive beyond Kuszczak that whistled past the Polish international at his near post.
Former Manchester United keeper Kuszczak, who joined Wolves on a short-term deal last November, was making his debut as a replacement for Carl Ikeme who will be missing for up eight weeks with a broken foot.
Pogrebnyak’s smart finish ensured that Kuszczak’s first action for the team was to pick the ball out of the back of the net.
It took Wolves some time to recover from that early setback but they eventually built up a head of steam with Kevin McDonald shooting into the side netting and Bakary Sako seeing his shot blocked before their spell of pressure finally brought its reward.
Wolves looked to have drawn level just before Afobe struck only for a spectacular save from Adam Federici and a goalline clearance from Nathaniel Chalobah to keep out a header from Sako following a Lee Evans corner.
But they were not to be denied seconds later when the ball found its way to Rajiv Van La Parra on the right wing and his centre was deftly headed past Federici by Afobe.
Wolves were in the ascendancy at this stage, but Clarke inspired his players to a stunning second-half performance that earned its reward through Williams’ classy finish.
Before he struck, Kuszczak had done well to deny Cox and Oliver Norwood either side of Michael Hector flashing a header wide from just six yards.
Reading’s spell of intense pressure looked set to come to nothing before Garath McCleary rolled the ball into the path of Williams whose perfectly placed 20-yard drive flew beyond Kuszczak and into the back of the net off his near post.
Their margin of victory would have been greater but for Kuszczak who tipped a goalbound shot from Nick Blackman around the post in the 80th minute.