Roach's young charges were twice forced to come from behind, with goals from Alex Parsons, Josh Wakefield and Elliott Ward earning them their second group one victory.
We worked hard in the week on trying to combat Swindon's style and it paid off, said Roach. To a point, they are fairly direct and the lads had to cater for that.
They worked very hard and their focus was excellent. We matched Swindon when we had to and played when we wanted to.
Roach also singled out defender Ryan Case for special praise when he said: Ryan had his best game for us. We worked with him on going back to basics and his performance was excellent. He grew in confidence as the game progressed.
Parsons touched home Wakefield's cross to cancel out Swindon's opener before Cherries again fell behind early in the second half.
But after Wakefield had restored parity, Ward's clinical finish following a well-worked build up involving Harry Bell saw Cherries seal victory.
Cherries: Murphy, Vokes, Strugnell, Case, Strickland, Wakefield, Ward, Bell, Farren (Makoni, 71), Hester, Parsons. Unused subs: Moth, Maybury, Tierney (g/k).