The 23-year-old had looked slightly rusty in her last 16 victory on Tuesday but was in superb form here to see Morake, who had received a bye to reach this stage.
The first round saw Marshall instantly assume control, using her jab to great effect and breaking through Morake's defences time and again - her left hook to the body proving particularly successful.
It was more of the same in the second round with the Botswanan fighter unable to keep Marshall at bay. Indeed, so dominant was the Hartlepool boxer that one judge scored the round 10-8 in her favour.
Marshall continued in the same vein in the final two rounds and appeared to start to conserve energy with victory all-but assured, holding back and looking to pick off Morake rather than go in for the kill.
The fight had been over as a contest long before the final bell went, even in this four round bout, and Marshall progresses to the last four having been awarded the fight 40-36, 40-35, 40-35 by the judges.
Her semi-final will take place on Friday evening and with Marshall looking in such ominous form it will take some effort to stop her reaching the gold medal contest.