The spectre of relegation continues to loom over Wanderers but they were a match for Saunders' former club, who still have an outside shot of making the play-offs.
Reading loanee Kaspars Gorkss was handed his Wolves debut and looks set to be a useful addition to the squad, but Bakary Sako was undoubtedly the visitors' most potent threat.
It was Wolves who looked the more sprightly in the early stages. Jamie O'Hara's strike was tipped away by Adam Legzdins and Sako's inswinging corner moments later found Danny Batth but his header drifted wide.
Derby's first meaningful attempt followed a flowing passing move which ended with Stephen Ward firing just off target.
Karl Henry's foul on Craig Bryson handed Derby a free-kick in a promising position, but Ward, who had scored in each of his previous three appearances, could only direct his shot into the hands of Carl Ikeme.
The hosts grew into the game as the half wore on and Batth had to be alert to block Bryson's effort from the edge of the box.
There was time before the break for O'Hara to hit a well controlled shot just wide from 20 yards out.
A wayward shot on the turn from Batth punctuated an otherwise entirely uneventful opening to the second half before Sako's drilled effort forced a strong save from Legzdins.
At the other end, Paul Coutts' half-cleared corner was fired back with interest by Will Hughes but his strike cleared the crossbar.
Ward appeared to shove Henry inside the penalty area in the final minute but referee Graham Salisbury was unmoved by the visitors' protests.
Ward very nearly rubbed salt in the wound but his free-kick deep into stoppage time was kept out by Ikeme.
Wolves, now winless in nine, remain hanging precariously just above the drop zone.