England striker Kane was replaced after being hurt when Lions defender Jake Cooper tried to block his shot after seven minutes.
Christian Eriksen, Kane’s replacement, opened the scoring with a finish into the bottom corner after Dele Alli’s chest down before Son scored either side of half-time.
Alli tapped home the fourth with substitute Vincent Janssen adding the fifth – his first from open play for Spurs – before Son completed his hat-trick with virtually the last kick of the game after a mistake by keeper Tom King.
Spurs join Premier League rivals Manchester City and Arsenal in the semi-final draw, which takes place at Stamford Bridge on Monday after the final quarter-final between Chelsea and holders Manchester United.
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