Williams, seeded 23rd, battled to a 6-4 6-7(7) 6-3 victory over her gritty 21-year-old opponent in a two-hour 40-minute contest at Arthur Ashe Stadium.
The match finished hours before younger sister Serena was set to begin her quest to complete the first calendar sweep of the four grand slams in 27 years when she faces Russia's Vitalia Diatchenko in the tournament's opening match under the lights.
Venus squandered three match points in the second-set tiebreaker as 85th-ranked Puig rallied from 6-3 down to win six of the last seven points to level the match at one set apiece.
Venus, at 35 the oldest player in the women's draw, also failed to close the deal when serving for the match at 5-3 in the second set.
"I give so much credit to my opponent," said Venus, who blasted home 18 aces and powered in 48 winners, cranking her serves up to 124 miles per hour. "It seemed like every time I got close, she came up with unbelievable shots.
"She played so well from behind which is a great attribute, so great things for her coming."
It was a gutsy performance by Puig on the U.S. Tennis Center's main stage, especially considering the gap in their experience.
Venus carried in a 64-13 U.S. Open record into the match, with career earnings of over $31 million, while Puig was 1-2 in her previous two appearances in the main draw at Flushing Meadows with career earnings of just over $1 million.
(Editing by Frank Pingue)
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