New manager Alan Knill watched as Bournemouth created enough chances to have beaten his side by a bigger margin.
Bournemouth were ahead in the second minute when Marcus Browning burst into the area and shot against the legs of goalkeeper Gary Montgomery.
The ball broke loose for Browning to head across goal for Steven Foley-Sheridan to crash home his fourth of the season from six yards.
Rotherham were still reeling when Bournemouth went further ahead in the 11th minute.
Dani Rodrigues crossed from the right for Foley-Sheridan to head against the post and James Hayter snapped up the rebound for his 14th of the season.
Rotherham only then began to provide some resistance and a long-range shot from Paul Hurst was pushed over the bar at full stretch by Bournemouth keeper Gareth Stewart.
Bournemouth suffered a major blow when in injury-plagued striker Steve Fletcher limped off after 27 minutes with a hamstring problem to be replaced by James Coutts.
Foley-Sheridan shot narrowly wide in the 33rd minute and an intended centre from substitute Coutts rebounded off the bar as Montgomery back peddled furiously.
Loan signing Jonathan Forte shot wide form the edge of the area and Rotherham attempted in vain to pull a goal back.
Rotherham at last began to emerge as an attacking force in the second half with Lee Williamson shooting into the side netting in the 48th minute and then over the bar in the 72nd.
But it was Bournemouth who always looked the more likely to score with Foley-Sheridan twice wasting good shooting chances and Montgomery denying Coutts with his legs as the Rotherham defence threatened to cave in.