The dangerous Cole Skuse unlocked the Doncaster defence after 25 minutes with a brilliant cross aimed at Wood, who had the easy task of heading past David Button.
Doncaster's task was made harder just minutes later as full-back Habib Beye was sent off for serious foul play against Skuse.
From the resulting free kick, Cisse doubled Bristol's lead after delivery from Neil Kilkenny.
Beye's dismissal continued to restrict Rovers' chances in the second half as Bristol narrowly missed opportunities to extend their lead through Wood and Richard Foster.
El-Hadji Diouf gave Doncaster a lifeline in the 75th minute as the former Liverpool forward headed in Simon Gillett's cross.
Rovers were denied a late equaliser as Billy Sharp's strike was saved by David James in the Bristol goal.