The former Aldershot marksman pounced on a loose pass after only two minutes to fire home his first league goal of the season and half-an-hour later he outjumped City keeper Donovan Ricketts to head home his second.
Defensive errors have cost City dear in their recent defeats to Hereford and Wycombe and D'Sane gratefully accepted Eddie Johnson's wayward pass to fire Stanley ahead with an accomplished right-foot finish.
City's anxiety was there for all to see and the visitors almost extended their lead when Ian Craney poked a shot wide of Ricketts and the goal.
The Stanley man was stretchered off with a leg injury as a result of his lunge, but the visitors were still on top and D'Sane wasted a great chance when he burst clear and shot wide minutes later.
City were stung into action and they went close to equalising when Stanley keeper Kenny Arthur blocked well at the feet of Omar Daley.
Arthur was happy to see winger Alex Rhodes shoot straight at him after a sweeping Bradford counter-attack, but amazingly he became the second Stanley player to be stretchered off with an injury soon after.
Replacement keeper Ian Dunbavin marked his arrival with an assist for D'Sane's second goal, but it owed more to Ricketts' shocking error after 32 minutes.
The tall Jamaican stopper should easily have claimed Dunbavin's boot upfield, but inexplicably he allowed slightly-built D'Sane to outjump him and nod the ball into the empty net.
Exasperated City boss Stuart McCall must have feared the worst when Dunbavin pulled off a superb point-blank save to keep out a Peter Thorne volley and only the fingertips of Ricketts denied substitute David Brown a third Stanley goal before the break.
The Bradford fans' half-time boos turned into incessant vocal backing after the interval but their efforts proved in vain as more sloppy defending allowed midfielder Andrew Procter to fire in Stanley's third after 61 minutes.
D'Sane rose unmarked to head down Peter Cavanagh's free-kick, but when the rebound fell to Procter he had time to guide the ball into the bottom corner of the net from 14 yards.