Williams, whose previous best in Tokyo was the quarterfinals in 2004, broke the 19-year-old Bouchard with a forehand down the line to go up 5-2 in the third set. She held on to win the match that lasted three hours at Ariake Colosseum.
"She played so well," Williams said. "She's going to be a great player
-- she's already a great player -- and it was just a fight to the end."
Williams will face either Svetlana Kuznetsova or Petra Kvitova in the semis.
"I was just fighting until the end," Williams said. "It was disappointing to lose the second set, but to win the third set is the goal, so I'm happy."
Kvitova defeated Madison Keys of the United States, 6-2, 6-2 while Kuznetsova beat Sorana Cirstea 7-6 (3), 6-1 in third-round matches.
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