Lampard and Tom Lawrence were both dismissed in the second half as the Rams were outclassed in South Yorkshire.
Ryan Manning's first goal for the club proved to be the difference but Rotherham should really have recorded their third home league win of the season more comfortably.
Rotherham had the first effort on goal after the ball fell kindly to Michael Smith, but the striker's effort dribbled just wide of the far post.
Tom Huddlestone was the first Derby player to come close as his driving effort from 25 yards had to be clawed away by Marek Rodak.
Both sides had chances to go in front during the first period but it was Rotherham who finished on top.
Richard Wood's header from Will Vaulks' long throw bounced over the bar before Richie Towell's volley had to be punched away by Scott Carson.
Smith had another effort fly into the side scoring before the break after he latched on to Ryan Williams' cut-back.
Rotherham picked up where they left off in the second half and Kyle Vassell had a stinging effort pushed out by Carson.
The flashpoint came just before the hour mark as Lawrence dived in horrendously from behind on Towell and deservedly saw red. A melee ensued with Lawrence ordered off the pitch and yellow cards were given to Vasell and Martyn Waghorn.
Rotherham did not have to wait long to make their advantage count after they were awarded a penalty for a clumsy foul on Vassell by Fikayo Tomori. Manning coolly tucked it away to give them a 63rd-minute advantage.
Derby boss Lampard looked to change the game from the bench and introduced three attacking substitutions but he soon had to find a place in the stands after leaving his technical area to complain about a 77th-minute decision.
His side pushed for a leveller but substitute Jack Marriott scooped an effort over the top. Fellow substitute Mason Bennett was then denied a sight of goal by strong defending from Semi Ajayi.
Rotherham chose to try to see out the game in seven minutes of added time instead of attempting to find a sealing goal. The policy could have backfired had Mason Mount's long-range free-kick been more accurate but the Chelsea loanee's effort flew over the bar and Rotherham clung on to three points.