The goal was tough on Derby who twice had to re-organise after losing both strikers with injuries.
Although West Ham began by pulling Derby all over the pitch, Andy Oakes made an outstanding save to deny David Connolly before Derby hit back.
Svensson had a shot on the turn brilliantly saved by David James in the 31st minute but he limped out of the action a minute before half-time and was soon followed by Morris.
But Derby were still well in the game and Ian Taylor headed over from ten yards in the 68th minute when West Ham were caught on the break.
Oakes made another good save from Connolly but the game was starting to drift until West Ham punished some hesitant defending to win a corner in the 89th minute.
Quinn drove the ball across the face of goal and Hutchison arrived to turn a right-foot shot past the helpless Oakes.
Even then, Derby might have snatched a point in injury time when Gary Caldwell crossed from the right but Taylor's downward header did not have enough power to beat James.