Liam Feeney opened the scoring for Bournemouth after 8 minutes with a 25 yard shot which deflected in off Scott Cuthbert.
On 21 minutes Paul Caddis equalised for Swindon, but then found themselves behind again on 27 minutes after Ings scored from a close range rebound to make it 2-1.
On 58 minutes Matt Richie equalised for Swindon with a follow up shot after Dossevi had hit the post, and then Caddis had his follow up shot blocked as well.
On 73 minutes Hollands scored the winner for Bournemouth with shot which went in off the bar.
This defeat leaves Swindon in the relegation zone going into Saturday's home game with Rochdale.