The 25-year-old Bulgarian, whose previous grand slam semi-final was at Wimbledon in 2014, will meet either Rafa Nadal or third seed Milos Raonic in the last four.
The pair engaged in a cagey baseline battle, as Goffin struggled with his serve and made 46 unforced errors.
Goffin saved two match points trailing 5-3 in the third set but Dimitrov was able to serve out in the next game and clinched the win in two hours, 12 minutes when he blasted a backhand winner down the line.
(Writing by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
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