The 19-year-old Montrealer lost 6-3, 6-7, 6-3 to Williams in a three-hour match.
Williams, playing in the Tokyo tournament for the first time since 2009, broke Bouchard with a forehand down the line to go up 5-2 in the third set and held on to win the match that lasted just over three hours at Ariake Colosseum.
Each player served a pair of aces and Willams recorded 35 unforced errors to 34 for Bouchard.
Bouchard had upset sixth-seeded Jelena Jankovic of Serbia 7-5, 6-2 on Wednesday, a day after ousting No. 8 Sloane Stephens of the U.S.
Bouchard, making her debut in the Tokyo tournament, is 46th in the world rankings. She earlier said winning last year's junior Wimbledon title has given her confidence to compete at a higher level.
Williams, who is 63rd in the world rankings, will face either Svetlana Kuznetsova or Petra Kvitova in the semis. The American had ousted top-seeded Victoria Azarenka on Tuesday.
Kvitova of the Czech Republic defeated Madison Keys of the United States, 6-2, 6-2 while Kuznetsova of Russia beat Sorana Cirstea Romania, 7-6 (3), 6-1.
_ with files from The Associated PressSuggest a correction