Mark Bradley set the ball rolling with a curling effort from 20 yards past Kevin Poole after half time.
The lead was added to by Kevin Ellison, who was brought down in the area and smashed home the resulting spot kick himself.
Albion pulled a goal back late on but the Millers went safely through.
In a bright start for the Brewers, they had a great chance to take the lead in the first minute when they broke quickly from an early Millers corner but Garyn Preen's effort was saved by Jamie Annerson.
After Jason Taylor received treatment for a cut behind his ear, The Millers nearly had a chance before the half-hour mark when Nicky Law released Jamie Green down the left wing but Andy Corbett intervened.
Burton then had two chances in quick succession when Greg Pearson fired over and drew a save out of Annerson with a low left-footed strike.
After the break Ellison almost opened the scoring when Corbett slipped as he went to clear a hopeful punt into the box at the far post which allowed the winger in, but as he appeared to be brought down, Poole collected the ball while the Millers protested.
However the opener wasn't long in coming, as Bradley broke the deadlock soon after when he curled home from just outside the area following Green's lay off.
A ball flicked on by Pope in the 78th minute then allowed Ellison to burst through on goal and he was hauled down by Corbett, scoring himself from the spot sending veteran Poole the wrong way.
Sub Richard Walker netted for Burton, firing under Annerson's body seven minutes from time but it proved just a consolation for the home side as the Millers advanced.