A brace from come-back man Lee Bradbury saw the Cherries produce consequective away wins for the first time this season.
Bournemouth were quick out of the blocks with Goulding bringing a smart save early on. Another half-chance came his way but he failed to test the keeper.
It took just five minutes after the break for the Cherries to break the deadlock. Pitman sent in a long cross that Bradbury volleyed home in style to give the Cherries the lead.
In a repeat of the first goal Goulding sent a cross across the box which landed at the feet of Bradbury who smashed home under the body of the keeper.
The Cherries played a containing game for the last quarter to secure a vital three points.