Williams, making her first appearance in the Tokyo tournament since 2009, broke serve to lead 5-3 in the third set at Ariake Colosseum. She then won with a crosscourt forehand that No. 13-seeded Halep hit into the net.
"It was a very tough match," Williams said. "She played very well. I don't know how I was able to win the match. I just wanted to stay in Japan longer."
Bouchard upset sixth-seeded Jelena Jankovic of Serbia 7-5, 6-2.
Making her debut in the Tokyo tournament, Bouchard broke Jankovic to go up 5-2 in the second set and then held serve to win.
Jankovic had a 5-4 lead in the first set but Bouchard won the last three games after a talk with her coach.
"I felt like I wasn't playing my best in the first set," Bouchard said. "But I stayed with her and started to get a lot more aggressive near the end of the first set and that was the turning point."
The 46th-ranked Bouchard won last year's junior Wimbledon title.
"That gave me a lot of confidence to play in the pros," Bouchard said. "Playing week in, week out against the top players has made me a better player."