World number one Williams extended her match win streak to 15 by beating the red-hot Bacsinszky 7-5, 6-3 on the Tennis Garden stadium court.
"She was on a winning streak, so I was like, 'I hope I win tonight, because she hasn't lost in a really long time,'" Williams said of Bacsinszky, who was came into the tournament off back-to-back WTA titles in Acapulco and Monterrey, Mexico.
Bacsinszky's fourth round win over Elina Svitolina was her 15th consecutive match win, including Fed Cup play.
Williams is playing in her first tournament since winning a sixth Australian Open crown in January, her 19th Grand Slam title.
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She is making a celebrated return to Indian Wells after being booed in the 2001 final. The hostile reception from the crowd resulted in Williams' 14-year boycott of the Indian Wells event but she now says she is happy to be back.
Bacsinszky, 25, has had her own personal demons to deal with after a bitter parting from her father.
She said her dad pushed her into tennis so he could live his dream through her. She even quit the game for awhile, but her successful return has been one of the feel good stories on the WTA Tour this year.
- Serena happy to get through -
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Williams got past her in one hour and 25 minutes. She belted seven aces but also had four double faults and said she needs to step up her game.