After an even opening to a bruising game which saw eight yellow cards and one red, Rovers took a 24th minute lead when Martin Foster's low shot was deflected past Dover keeper Paul Hyde.
Hyde, barely fit to play because of an ankle injury, was left rooted to the spot when Forest Green's Kayode Odejayi slotted a low shot inside Hyde's left-hand post from the edge of the area in first-half injury time.
The goal seemed to knock the stuffing out of Dover and the game was virtually over as a contest after just two second-half minutes.
Dover defender Steve Norman was perhaps harshly adjudged to have handled in challenging for a header in his own area, and Neil Grayson sent Hyde the wrong way from the spot.
Dover substitute Andy Arnott, just back from suspension, was dismissed after just 20 minutes on the field for a two-footed tackle on Matthew Russell who was taken off injured.
Dover's best chance of pulling a goal back fell to Matt Carruthers but he dragged his shot wide when clean through on goal.