The Millers were drawn against the Premier League outfit in their first involvement in this year’s competition and locked horns in the North East in midweek.
The hosts started brightly and Connor Malley set the ball rolling for the hosts after 12 minutes before Marcus Tavenier doubled their advantage minutes later to establish them an early lead.
It remained that way until half time with the Millers getting a foothold in the game prior to the interval, but a brace from Stephen Walker following the restart either side of Jack Lambert’s looping effort ensured Boro would progress to round four.
Middlesbrough: Hemming; Convery, Reading, Hegarty (Holdsworth 81), Cook. Renton, Lambert, Tavernier (Wilson 75), O’Neill, Malley, Walker.
Unused: Brynn (gk); Guru, Storey.
Rotherham: McMahon; Southern-Cooper, Hinds, Murr, Saxton (Sterling 79), Naeem (Atherton 16), Maguire, Wiles, Kayode, McCarthy (Mvumbi 55), McGinley.
Unused: Fidler, Martin.
Referee H. Conley