There was not a shot on target in the first 25 minutes in Suffolk, but when the goalscoring chances did come, they fell almost exclusively to the Tractor Boys.
Tommy Smith, who had earlier required treatment for a head injury and returned to the field sporting a bandage, climbed above Jack Butland to nod a looping ball over the Barnsley keeper and the crossbar.
It was Town's top goalscorer who opened up the Barnsley defence again when he flicked cleverly into the path of Aaron Cresswell, whose drive towards the near post was turned behind by Butland.
Cresswell's delivery from set pieces also caused the Tykes problems throughout the first period, with Luke Chambers having gone close before Murphy made use of the full-back's threatening corners.
The Republic of Ireland international lost his marker, Reds captain Martin Cranie, and climbed highest at the far post to power a header beyond Butland and into the net on 41 minutes.