Williams, 39, eased past Chinese sixth seed Qiang Wang, who is 12 years her junior, 6-3 6-2 and will meet Barty for the second time in her long career.
Despite the prize at stake, Barty looked calm and composed throughout the final against doubles partner Goerges on Sunday, just as she did when beating Marketa Vondrousova in the Roland Garros final a fortnight ago.
The US and Australian Open champion now runs the risk of heading into Wimbledon short of match practice on the grass as she has not signed up to play in Eastbourne next week.
Barty saved two break points early in the first set but she made no mistake when she was offered the opportunity - Goerges putting a backhand wide to give the Australian a 4-2 lead.
She trailed 5-0 in the first set and even bizarrely chose to sit on the court instead of her chair at changes of end.
Barty will finish the week ranked world No 1 if she wins the title after Osaka suffered a disappointing loss to Yulia Putintseva.
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Second-seed Barty went safely through to the quarter-finals as a 6-3 6-1 victor against American Jennifer Brady but must capture the title on Sunday to depose Osaka.
Should Barty lift the title, she will usurp Australian Open champion Osaka and become only the 27th woman in 49 years to hold the No 1 ranking and head to Wimbledon as the top-seeded player.
"That's what we have been able to do over the last month in particular, but, yeah, I mean, I feel like I'm comfortable in my own skin. I feel like I know exactly how I want to play in most matches, and it's just about going out there trying to execute as best I can".
Only the rain threatened to slow Barty as it delayed the start of the match and then briefly interrupted the second set.
She recovered from 3-0 down in the second set and saved a set point serving at 4-5 to see off Goerges, the world No.19 and a Wimbledon semi-finalist previous year, in one hour, 28 minutes.
Barty will be in select company if she wins, as the only other women to follow a singles title at the French Open with a victory on a British grass court in their next event are Serena Williams, Steffi Graf (four times), Martina Navratilova, Chris Evert and Margaret Court.