Stanley's faint play-off hopes took another knock as they slipped to their third defeat in a row as promotion-chasing Cherries moved into the automatic places.
The Reds mustered little in attack at Dean Court with Eddie Howe's side dominating proceedings and the Reds were lucky to keep it down to two.
The home side opened the scoring when Danny Hollands throw was only half cleared by Dean Winnard and Liam Feeney fired past Ian Dunbavin on 18 minutes - although Cherries striker Brett Pitman claimed it had taken a nick off him.
The home side missed some decent chances but made the game safe on 79 minutes when Feeney outstripped the Reds defence and powered in a fierce shot which Dunbavin could only turn onto his crossbar and it dropped down invitingly for Pitman to tap home his 20th goal of the season.
John Coleman's side hardly tested Bournemouth keeper Shwan Jalal with strikers Bobby Grant and Billy Kee struggling to create chances and sub Gary King only forcing Jalal into action in injury time.
Coleman kept his players in for a 45 minute inquest after the game and said: "We weren't good enough - Bournemouth didn't have to get out of bed to beat us. I think we had three shots in the whole game. The second goal was a calamatious error just when we were having our best spell in the game.
"But over the 90 minutes we weren't good enough and we got what we deserved.
"We have been having a huge discussion about why we didn't create chances. I have got to take some of the blame as I gambled that the lads I played on Tuesday would give me a response today as I played with the same side but it was possibly an even worse performance.
"It's a test of my managerial skills now, I have only got 19 players to pick and choose from and we have got to try and get back to the threat I know we are as that's not the Accrington Stanley I know.
"I can guarantee you one thing - there will be changes on Tuesday against Barnet."