The top seed took 10 games in a row to win 4-6 6-3 6-0 and set up a final against Lucie Safarova on Saturday.
Williams, 33, has been unwell throughout the tournament and struggled as temperatures soared in Paris.
"I don't think I've ever been this sick," Williams told ESPN. "I didn't expect to win that, I really didn't."
She added: "I got the flu after my third-round match and I've been really struggling ever since then. Hopefully this is the worst and I'll get better from here.
"I thought, 'If I'm going to lose, I'm going to go for winners.'
"The next thing I know it was a set all and I thought, 'I really don't feel like playing a third set.' I was so tired. I just fought for every point and here I am."
England 6-Russia )
England defeated New Zealand 49-46 to level up the three-match Series at 1-1 heading into the deciding match on Wednesday morning.