The Millers soaked up plenty of early Burton pressure with Everton loanee Nathan Broadhead rattling the post inside the first minute and Scott Fraser firing over from close range for the Brewers.
The 24th-minute goal had an element of fortune, with midfielder Ben Wiles making room inside the box for a shot only for a deflection to take it onto the post and bounce off the Albion goalkeeper before nestling in the back of the net.
Kyle Vassell struck the crossbar for the visitors with an ambitious effort from wide on the left before Rotherham keeper Daniel Iversen reacted superbly to keep out a Liam Boyce header.
Albion were denied what appeared a clear-cut penalty in the 68th minute when Fraser was felled by Richard Wood after bursting into the box on the end of a poor defensive header.
Broadhead missed a great chance in stoppage-time to grab an equaliser but fired over from Boyce's cross before substitute David Templeton volleyed against the crossbar.