Rotherham dominated the game with striker Jamie Clarke causing the Imps defence problems with his pace down the left and he went close to opening the scoring in the 24th minute when he cut inside before firing at keeper Rob Burch.
The Millers kept up the pressure in the second half and grabbed the decisive goal in the 65th minute.
Clarke saw his effort blocked before the ball fell for Cummins who was left with the easiest of tap-ins and made no mistake.
United kept looking for more goals and substitute Ryan Taylor wasted two good chances late on.
Jamie Green almost added a second in stoppage time when he beat Burch with a powerful shot only to see his effort come back off the bar.