Paul Lambert named a strong team for the second-round clash and first-half goals from Andreas Weimann and Christian Benteke ensured the Millers would not be causing an upset.
The visitors came into the match more after the interval but were hit on the break when Benteke set up Fabian Delph to make it three and effectively end the game as a contest.
Lambert branded the two-legged semi-final defeat to Bradford last season as his lowest point as Villa boss, and he was not prepared to risk it happening again.
In truth, they were far too good for Steve Evans’ side, with Lambert’s selection justified by half-time as Weimann opened the scoring with a fine 20-yard effort in the 19th minute and then Benteke headed home Agbonlahor’s cross 20 minutes later to ease the nerves.
Delph put the game to bed shortly after the interval with a fine team goal, latching on to Benteke’s scooped pass to finish with aplomb.
It could have been a greater margin of victory, but Villa were wasteful in the final 30 minutes, with Agbonlahor and Joe Bennett missing good opportunities.
Although well beaten in the end, the Millers acquitted themselves well, particularly in the first half, where Alex Revell could have twice given them the lead, while Michael O’Connor’s curling free-kick which went just over was the highlight of their second half.
As it was, Villa made safe passage through to the third round where they will face a home tie against Tottenham.