Williams was humbled by Simona Halep the previous day, when the 18-time Grand Slam champion won only two games.
She turned around and eliminated Bouchard from semifinals contention with a 0-3 record in the round-robin stage, while Williams improved to 2-1. The American will have to wait until Friday's match between Halep and Ana Ivanovic to know if she is through to the semis.
Williams will make the final four unless Ivanovic manages to beat Halep in straight sets. Halep is guaranteed of a semifinal berth.
Meanwhile, the outcome of the other group remains uncertain, with none of the four players qualified for the semis, and none out of contention.
Petra Kvitova beat Maria Sharapova 6-3, 6-2, further eroding the Russian player's hopes of claiming the year-end No. 1 ranking.
Sharapova, who needs to win the title and rely on Williams not reaching the final if she is to bump the American from the top spot, fell to a 0-2 record while Kvitova is 1-1.
In order for Sharapova to progress to the semis, she will need to win her last match against Agnieszka Radwanska and rely on Caroline Wozniacki beating Kvitova, and have both matches decided in straight sets.
Williams credited her coach Patrick Mouratoglou with lifting her out of the doldrums and preparing her for Thursday's match.
"I started to believe that maybe I could come play another match," Williams said. "I wasn't quite sure that I could.
"I was feeling mighty low. I was able to feed off this belief. I know that sounds weird, even though I've won so many titles, I still at some point feel like, 'Oh gosh, maybe I might not be able to do this or maybe I might not be able to do that?'"
Williams was fatalistic about whether she will make the semifinals and remain in the running for a third straight title at the season-ending championships.
"If I wanted to win and be a part of the event, I should have won my match yesterday or should have done better," Williams said. "If I don't qualify, I'll be sad, but it wasn't my year. I'm not going to fall out and die."
Bouchard, the Wimbledon finalist, came into the tournament with only two tour matches in a month due to injuries, and won only 11 games across her three matches.
"I didn't have ideal preparation but that can happen to a number of players at any given tournament," the Canadian said. "Disappointing that it's at such a big and cool event where I would love to play as well as I can."
Sharapova, who lost the Wimbledon final to Kvitova in 2011, beat the Czech left-hander in their past five meetings and started brightly by winning the opening two games. But Kvitova took over from there, winning 11 of the next 12 games.
Kvitova said she was feeling burnt out during her opening loss to Radwanska, so took an unusual approach to freshen up for Thursday.
"When I lost against Aga ... I was so tired and sick of the tennis for a moment," Kvitova said. "So I didn't practice today at all, and I just really relaxed and cleaned my mind a little bit."
Earlier, Wozniacki moved closer to a place in the semis by beating Radwanska 7-5, 6-3 for her second win in the group stage.
The first set, which began with four service breaks in five games, lasted 67 minutes and contained some lengthy rallies that were punctuated by superb shot-making.
Radwanska ended up the loser but played a couple of extraordinary volley winners: One picked up at her shoelaces and lifted diagonally over the net, and another leaping effort played with her back to the net.
"I just needed some more good serves as well in that match," said Radwanska, who has a win and a loss.
Wozniacki was able to smile after Radwanska's trick shots.
"I'm like, 'OK, you know what, that's just too good,'" Wozniacki said. "You can either get frustrated or laugh — it's better to laugh."Suggest a correction