Will Grigg broke the deadlock five minutes after half-time, pouncing from barely a yard out after home goalkeeper Scott Flinders made a mess of keeping out Dan Barlaser's low drive.
Rarmani Edmonds-Green then wrapped things up with a fierce finish to double the Millers' advantage on 75 minutes.
Meanwhile, Doncaster Rovers claimed a much-needed victory at home to MK Dons, but remain rooted to the foot of the table.
Tommy Rowe moved Richie Wellens' men ahead on six minutes, though a Peter Kioso goal restored parity mid-way through the opening period.
With the game still level heading towards the final 10 minutes, Rovers introduced striker Tiago Cukur from the substitutes’ bench.
And that move proved to be a shrewd one as the Turk applied a finishing touch to Jordy Hiwula’s goal-bound effort to decide matters within 60 seconds of his arrival on the pitch.