Danny Batth pounced with a perfectly placed 48th-minute header and Dave Edwards then made the game safe from close range after 69 minutes as Kenny Jackett’s side secured their 13th win in the last 16 games.
They could even afford the luxury of seeing Bakary Sako miss a 73rd-minute penalty that he crashed against the crossbar after Nouha Dicko had been fouled by Michael Bostwick.
In the process they also collected their 23rd clean sheet in the league this season – equalling the record set in the 1923-24 season.
Peterborough arrived at Molineux seeking to strengthen their position in the final play-off spot but they struggled to carry a threat with their 29-goal striker Britt Assombalonga starved of any real clear cut chances.
Batth made the decisive breakthrough when he met a right-wing cross from Sam Ricketts to beat goalkeeper Bobby Olejnik from six yards out.
Edwards then stabbed the ball home from close range after Olejnik had saved a Sako free-kick.
The margin of victory would have been greater but for Olejnik who pulled off smart saves from Sako, Dicko and Ricketts.
Peterborough were then denied a consolation strike eight minutes from time when Carl Ikeme pulled off a spectacular save to deny Bostwick after he had left fly from 30 yards out.