First-half strikes from Leigh Griffiths and Edwards ended Tranmere’s recent revival and earned Wolves a fifth win in their last seven league games.
Tranmere, who had hammered Coventry 5-1 in their previous game, had arrived at Molineux on the back of a five-match unbeaten league run.
But their hopes of extending that sequence disappeared when goalkeeper Owain Fon Williams literally handed Wolves the lead in the 17th minute.
There appeared to be little danger when Griffiths tried his luck from fully 30 yards. Fon Williams looked to have the shot covered, but somehow let the ball squirm from his grasp and over the line.
There was no way back for Tranmere after that and their fate was sealed by Wales international midfielder Edwards three minutes before half-time.
After Griffiths had seen his header deflected wide for a corner, Edwards rose above the Tranmere defence to head home Bakary Sako’s corner.