Trailing 6-3 from Tuesday's opening session, Gould won seven of nine frames here on Wednesday to win 10-8 and set up a second round clash with Judd Trump, who defeated reigning champion Neil Robertson in the first round.
It was a painful case of deja vu for Fu, who was beaten 10-9 by Gould at the same stage of the World Championships last year.
Fu had shown inspired form in the early stages of the match, but fell to pieces with the second round within touching distance.
Gould reeled off five frames in a row to lead 8-6, and it could have been 9-6 but the 29-year-old wasted an early chance in the 15th frame.
He managed to blast the black at a corner pocket so firmly it jumped off the table and landed on the Crucible carpet, to his bemusement.
Fu narrowed the gap to 8-7 with a run of 60 and then drew level with a break of exactly 100, but a run of 59 helped Gould jump back into the lead, and he finished with a flourish to book the appointment with Trump.
Fu admitted his lack of consistency had been to blame for his latest failure at the Crucible Theatre.
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