Early breaks of 87 and 75 helped Fu take the opening two frames before Higgins responded with a century.
But further scores of 79 and 66 saw Fu coast across the finish line to set up a last four meeting with Gerard Greene, who edged an untidy affair with Mark Allen 4-2.
It is only the second time in a 21-year professional career that Greene has reached the semi-finals of a ranking event.
"The last few years have been pretty bad really, I've played great one day and terrible the next," Greene told World Snooker.
"I kept getting beat in deciding frames, and some players have been playing fantastic against me, not missing a ball. The confidence was zero at one point."
Judd Trump also booked his spot in the last four after battling back to beat Joe Perry 4-2.
Perry established a 2-1 lead with back-to-back centuries – including a 133 in the second frame – but Trump edged ahead by taking the next two.
And although Perry notched a half-century in the sixth, it was Trump who prevailed 66-56 to progress.
In Friday's late contest, Barry Hawkins beat Yu Delu 4-1.
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- Gerard Greene
- Judd Trump