It was Dale's sixth defeat in their last eight games and allowed Bournemouth to leapfrog them into second place in the League Two table.
Burton's best effort in the opening 45 minutes at Spotland was a 25-yard volley from Cleveland Taylor but Dale goalkeeper Kenny Arthur dived full stretch to his left to push the shot round the post.
Taylor's luck was in after the break when his 62nd minute cross dipped over Arthur and into the net.
Four minutes later Burton doubled their advantage when Craig Dawson felled Steve Kabba and Shaun Harrad sent Arthur the wrong way from the penalty spot.
Gary Jones saw a thumping drive saved by Kevin Poole before O'Grady netted a consolation, making the goalkeeper pay for hesitancy and lofting one into an unguarded net.