World number one Robertson looked set for a classic battle with world number two Selby, the local man edging the opener 73-65 then losing three of the next four frames as Selby clattered in breaks of 68, 63 and 76.
Just as Selby looked to be in control of the game, however, Robertson went up a gear, levelling the match with an 86, clinching two slightly scrappier frames to pull 5-3 ahead, then finishing in style with a break of 138 to come out a 6-3 winner and clinch a place in the final against Fu.
In the first semi-final Hong Kong's Fu had beaten Robert Milkins 6-4.
Fu took charge of a scrappy match quickly, racing into a 4-1 lead after a series of error-strewn frames in which both players had chances.
Milkins then reeled off three frames in a row to level things before a break of 60 put Fu ahead once more.
The 10th frame was a nailbiting thriller that could have gone either way, but it was Fu who held his nerve best to edge it 51-49 on the black and set up a final against Robertson.
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