The world number two, will play either Mark Allen or Shaun Murphy in Sunday's best-of-17 final.
A break of 74 in the opening frame got Selby off to a perfect start, and he claimed the first three frames while conceding just nine points.
Fu got into the match after that, but ended up going 4-0 down as he lost the fourth frame 60-50.
That failure seemed to fire up the Hong Kong star, who won four of the next five frames - thanks in part to breaks of 104 and 70 - to make a contest of it.
And it looked as if he would level the match to force a decider as he led 58-31 in the next frame, but a mistake let Selby in - and the Jester from Leicester cleared up to claim the match.
- Sports & Recreation