Both goals saw Forest goalkeeper Muric left red-faced as their new head coach Sabri Lamouchi endured a frustrating first game in charge.
The plot of the first half was underpinned by those errors.
The Reds had taken the lead following a bright start as Cash drove a shot inside the near post following a neat exchange of passes with Albert Adomah.
But West Brom took just seven minutes to equalise as on-loan Manchester City goalkeeper Muric made his first mistake.
Edwards had shown quick feet to dance into space in the box and find the room to let fly with a shot. It was straight at Muric but he somehow allowed the ball to slip from his grasp and into the back of the net.
Things got worse for the Forest stopper, who then saw a cross from Phillips loop high over his head and inside the far post to make it 2-1 to the visitors in the 26th minute.
It was not intentional from the Baggies winger, but he still happily celebrated as a dejected Muric had to pick the ball out of the back of the net for a second time.
The goal completely changed the mood at the City Ground, where the home side had started well.
Muric was one of four Forest debutants, along with Alfa Semedo and Tiago Silva in midfield and winger Albert Adomah.
There were five new faces in the Baggies line-up in the form of defenders Nathan Ferguson and Semi Ajayi, midfielders Romaine Sawyers and Filip Krovinovic and forward Kenneth Zohore.
A familiar battle resumed after the break, with Muric this time coming out on top as he made a strong save to deny Edwards a second goal.
Semedo shot high and wide following a superb run, while a cross from Adomah almost picked out Lewis Grabban in the centre.
Substitute Sammy Ameobi headed wide late on as the Baggies held out.