Despite taking the lead through Tom Pope's first half header against the run of play, the visitors ran riot in the second half and dominated in the final third.
Danny Hollands netted twice after Brett Pitman levelled just after the break as the Cherries crowned a convincing night with three points.
After Bournemouth looked the brighter side in the first period, Pope's header from a Marc Joseph cross on the right gave the Millers a slender half time lead shortly after they had a clear penalty decision waved away after Rhoys Wiggins' handball on the line.
But Pitman skipped round Pablo Mills' challenge to beat Andy Warrington two minutes after the interval to deservedly level affairs.
Hollands then drove into the corner with a crisp 20 yard low shot on the hour mark, and netted again to seal the win seven minutes later as he tapped home Steve Fletcher's knock down from Pitman's corner leaving the Millers to lick their wounds ahead of the weekend game at Darlington.