In the second half with the scores still at 0-0 Swindon made a half time sub with Andy Nicholas coming on to replace the injured Sammy Igoe.
Bournemouth took the lead on 51 minutes when O'Connor headed in a cross from close range.
Bournemouth's lead didn't last long as on the hour mark Sean O'Hanlon scored from 10 yards out after a cross from from Andy Nicholas came to Parkin, who then passed the ball to O'Hanlon.
After 70 minutes the referee was replaced by the 4th official after going off injured which delayed play by about a minute.
On 76 minutes Bournemouth scored their winner when Shaun Maher scored from close range after a corner.
Swindon had a few late chances, but didn't manage to get a second goal. Overall it was a better game than the last few Swindon games, which Swindon should have got at least a draw from. Swindon move move out of the top half of the table for the first time since August.
Swindon's next game is away to Peterborough on Boxing Day, with a 3pm kick off.