PLAY-OFFS-bound Rotherham showed few signs of complacency despite their place in the top six being virtually assured before kick-off at the New York Stadium.
The Pirates looked on the beach in the first half as they were sunk by Michael Smith's early strike and substitute Caolan Lavery's 90th-minute tap-in..
They showed more spirit after the break but rarely looked like plundering the points.
Millers chief Paul Warne made just one change to his starting line-up, following the midweek 1-0 win at Gillingham.
Joe Newell replaced Ryan Williams in midfield as Smith was left as the sole striker again.
Mid-table Rovers made a couple of changes, opting to employ two strikers in Ellis Harrison and Tom Nichols.
The Millers struck in the ninth minute. James Clarke failed to control a throw-in back to him near halfway and was robbed by Smith, who burst down the left channel before expertly curling the ball past Sam Slocombe into the far corner.
Will Vaulks went close twice within a minute, seeing one effort deflected for a corner, from which he struck the ball first-time a foot over the bar.
Rotherham continued to control possession without adding to their tally before the break.
Richie Towell hooked over from Smith's miscued shot at the start of the second period and Newell's first driving run of the game saw him go down in the area but without winning a penalty.
Bristol's best chance came as Byron Moore got in front of Vaulks and sped into the area only to mishit his shot as Marek Rodak raced out to dive at his feet.
Towell, who had been quiet, was replaced by Lavery in the 58th minute before Williams replaced Jon Taylor.
Bristol also made a couple of substitutions as they belatedly tried to press.
Williams, however, failed to make proper contact on a low cross to the near post from Newell before a groggy Matt Palmer, floored in midfield, was replaced by Semi Ajayi.
Bristol also replaced Harrison after he had been booked for leading with the arm against Richard Wood for a second time.
Kyle Bennett had a chance as he burst onto a ball down the middle but Rodak was out to block.
Lavery, however, made the game safe as he guided the ball in from Newell's deflected clipped cross from the left into the six-yard area.