The 34-year-old, seven-times grand slam winner reached the round for the first time in four years at Flushing Meadows through a 6-1 6-4 victory on the Arthur Ashe Stadium court which she helped christen with the first Open final there in 1997.
"I was watching Serena last night and she played so well so I tried to do the same thing," twice U.S. champion Venus said about her 32-year-old, number one-ranked sister, who blazed by fellow American Taylor Townsend in straight sets on Tuesday.
"I'm really happy to have pulled it out in the end," added Venus, who will play Italian 13th seed Sara Errani who beat Australian Anastasia Rodionova 6-4 7-6 (2).
Williams charged through the first set, but the next set stayed on serve until the ninth game when the 78th-ranked Swiss hit a wayward backhand wide to put the American 5-4 ahead.
With Williams serving for the match, Bacsinszky reached break point at 30-40 threatening to put the match back on serve.
But the 19th-seeded Williams then powered in a 96mph second serve, her fastest second serve of the match, for a winner.
"When the stakes get higher I start to hit harder," Venus said. "I can't help it, it's instinct for me.
"Sometimes it's not the smartest thing, but sometimes it works."
Williams's appearance marked 17 years since she helped christen the massive Arthur Ashe stadium centre court as a 17 year old in 1997, waging the first final staged there in which she lost to Martina Hingis.
"I didn't know what I was doing, that's what I remember most," recalled a laughing Venus. "I don't know how I got to the final, I had no strategy.
"But it was a wonderful time. My family was here just as they are today so that feels great."
(Editing by Greg Stutchbury)
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