Seven points adrift of safety and needing to win to keep their slim hopes of staying up alive, United started on the front foot with ex-Bournemouth target Craig Fleming seeing his header cleared off the line by Marc Wilson following an in-swinging corner from Martin Woods.
The Cherries were slow out of the blocks but soon rallied and went ahead from their first raid on 12 minutes.
David McGoldrick, on loan from Southampton, lashed home a cracking 25-yard volley - his fourth goal in eight games - after good work by Wilson and Steve Fletcher.
The strike deflated the home fans and settled the Cherries, seeking to end a run of five successive defeats at Millmoor and they doubled their tally 16 minutes later.
Wretched defending saw the Millers switch off from Darren Anderton's corner and, after the unmarked McGoldrick saw his point-blank header parried by Neil Cutler, James Hayter followed up to fire in the loose ball for his 11th goal of the campaign.
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Having no doubt received some harsh words at half-time, the Millers came out of the traps with intent on the re-start with O'Grady's looping header flashing just wide.
The Cherries soon re-asserted their control with Fletcher heading straight at Cutler before O'Grady fired a rising shot over the top.
Hayter almost wrapped up the points for the Cherries when he saw his spectacular volley beaten away in splendid fashion by Cutler.
O'Grady and Henderson blazed half-chances over the bar and the closest United came to reducing the arrears arrived in the 74th minute with O'Grady, goal hero against Blackpool in midweek, seeing his stinging low shot well saved by Moss.
Bournemouth, whose first away win didn't arrive until February, almost added the icing on the cake late on with veteran striker Fletcher heading against the bar following Hayter's inviting cross.