The visitors played most of what little football there was in a low quality first half which never set the pulses racing.
A 15th minute shot by Grant McCann was charged down in the Stoke goalmouth to lift the small band of visiting fans.
And Kayode Odejayi missed the chance of the half in the 25th minute when he headed Brian Howard's cross into the side-netting.
Stoke's passing was awful in the first period and a half-hit shot by Jon Parkin, easily collected by Muller, was the best they could muster.
The home side couldn't be as bad in the second half and they did instil more gusto into the game, even though the quality still left much to be desired.
Stoke were finally cranking through the gears by the 56th minute when Ricardo Fuller headed Jody Craddock's cross against the top of the crossbar.
And full-back Stephen Wright forced a terrific save from Muller in the 68th minute when his 25-yard shot looked destined for the bottom corner of the net.
Barnsley were now under the cosh for the first time and Richard Cresswell should have put City ahead just a minute later.
Fuller was the instigator with a surging run down the right and Cresswell blasted over from the striker's cross with the goal at his mercy.
Stoke's surge continued and Muller - an impressive summer signing from Norwegian club Lillestrom - bettered his earlier effort from Wright when he produced razor-sharp reflexes to deny Dominic Matteo.
More desperate defending followed in the closing stages before City substitute Peter Sweeney belted a volley inches over the top with virtually the last kick of the match.