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Emyr Huws also had a go from distance early on, but the midfielder's effort was again stopped by Green with ease.
It was the visitors who took the lead in the 14th minute when Morrison bent in a free kick with his right foot into the top corner.
City tried to respond through Huws, who sent in a stinging effort from outside of the box, leaving Green to get across and tip it away from his top corner.
The visitors sought to increase their lead after half time, but Doyle saw his long-range effort saved at the bottom corner of the City goal.
QPR continued to search for an extra goal and they finally found it in the 73rd minute. Jermaine Jenas played in Morrison, who tucked the ball into the bottom corner from the centre of the box.