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  World number one Selby, the 2014 champion, looked impressive as he went 3-0 ahead with half-century breaks in frames two and three.
  Hong Kong's Fu hit back with a 72, and the pair shared four frames after the mid-session interval.
  China's Ding Junhui leads Alan McManus 6-2 in the other semi-final.
  Both Ding and Fu are hoping to become the first Asian player to win the sport's showpiece event.
  But Fu's chances appear fainter than Ding's after a characteristically dogged effort by Leicester's Selby in the best-of-33 contest.
  World number 14 Fu began anxiously, perhaps affected by the late jitters that saw him surrender a 9-1 lead in his 13-11 win over Barry Hawkins.
  Selby won a scrappy opener in which both men wasted a couple of chances, and he also took the second frame with a diligent 56.
  At 3-0 behind Fu made the most of a decent opening to score a well-constructed 72 before pinching a thrilling fifth frame full of incredible escapes, missed chances and numerous flukes.
  A 31-minute frame then went Selby's way for him to lead to 4-2 before they shared the final two frames, Fu with a fluent 89 and Selby scoring 69.
  Fu fought back impressively to keep alive his chances of going one better than Thailand's James Wattana - the first player from Asia to reach the last four at the Crucible.
  In 1993, the same year as the first of Wattana's two appearances, McManus graced that stage of the event for the second time
  But, 23 years on, the veteran Scot's hopes of progressing further look slim.
  Ding was in intimidating form from the start, opening with a break of 100 and scoring two further tons and two half-centuries to go 5-0 up.
  McManus, at 45, the oldest man to reach a Crucible semi-final since Ray Reardon in 1985, had scored just 47 points.
  But he showed his tactical nous to win two lengthy frames and get back to 5-2, before Ding ended with a 128.
  McManus did little wrong in the first five frames, but had every minor mistake punished by the world number 17.
  Ding had to win three qualifying rounds to reach this stage, but seems to have benefited from the extra table time.
  The 29-year-old has looked increasingly sharp, and has stayed fresh thanks to his fluent form which earned him an extra day's rest for beating Mark Williams inside two sessions in the quarter-finals.
  John Parrott, 1991 world champion: "Ding was superb. His break building and his match play has been fantastic. But I think he needed to win the last frame. The way he dominated the session, if he hadn't come out of it at least 6-2 he would have been kicking himself."
target: Mark Selby made the most of a tentative start by Marco Fu to build a 5-3 lead in the opening session of their World Championship semi-final.