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The US appeared headed for defeat after John Isner slumped to a 6-3 6-2 loss to Jo-Wilfried Tsonga and Williams dropped the opening set against Mathilde Johansson.
But from 4-1 down in the second set, Williams launched a stunning fightback, beating Johansson 3-6 7-5 6-4 in 139 minutes to keep the US in the tie.
Williams then teamed with Isner to win the mixed doubles 6-7 (7-5) 6-2 10-8 (match tiebreak), giving the US their second win of the tournament after their first-up victory over South Africa.
The second-seeded US will secure a spot in Saturday night's final if they can defeat Spain's pairing of Fernando Verdasco and Anabel Medina Garrigues on Thursday.
"Once again Venus was the MVP, I leaned heavily on her," Isner said.
Williams said she never doubted her ability to fight back against Johansson.
"I always believe in myself. That goes a long way," Williams said.
"At that point (when I trailed in the second set) I was thinking 'man, I've got to work on my game. The Australian Open is coming up'.
"I didn't want to let my team down."
Meanwhile, Isner said he wasn't freaking out despite starting the summer with losses to Tsonga and South African Kevin Anderson.
The 206cm power-hitter cut a frustrated figure for much of the 55-minute contest against Tsonga, with his mobility compromised at times by a slight knee injury that he has carried in recent times.
But the world No.14 was adamant his preparation for the Australian Open remained on track.
"Normally it takes me a while to get going. I'm not worried about it," said Isner.
"I remember about three years ago when I first played this event, I didn't play so well here but I won the next tournament.
"I have time to get ready and I'm confident going into the season. I've put in good work during the off-season.
"It certainly wasn't my best performance (against Tsonga). But I'm not freaking out about it.
"My knee's been bothering me a little bit but it's fine. It's a little tendonitis or something."
Tsonga, who made just four unforced errors compared to Isner's 21, was pleased with his early-season form, which included a straight-sets win over Spain's Fernando Verdasco on Sunday.