Gimelstob, ranked 151 in the world, outslugged the 30th-ranked Australian 7-6, 4-6,7-6 in a match lasting nearly two and a half hours to carry the US team to an unassailable 2-0 lead and a place in tomorrow's final.
"That was a big win, probably the biggest of my career so far," the New Jersey-born right-hander said after his first singles victory in Perth.
Chanda Rubin, the world No 17, who has not lost a singles tie in the eight-team tournament, had accounted for Nicole Bradtke 7-5, 6-0 to give the US team the early advantage.
Gimelstob, 19, arrived in Perth only nine hours before his first match against Guy Forget on Sunday. He was on a beach holiday in Florida when he was called up as a late replacement for Richey Reneberg, whose wife was due to give birth.
Gimelstob turned professional last June and his previous best performance was a quarter-final place at the Scottsdale tournament in the United States last year.
In the other Group A tie, the top seeds, Croatia, who lost 2-1 to the United States in a seven-hour match on Wednesday, were handed a 3-0 victory by France after Guy Forget forfeited due to blisters on his hand. Romania kept alive their chances of reaching the final with a 3-0 victory over Germany in Group B.
The top seed Thomas Muster, angered by mobile phone users, dropped a set and took more than two hours to beat Norway's Christian Ruud for a place in the quarter-finals of the Qatar Open in Doha.
The Austrian needed two hours and 13 minutes to defeat Ruud 6-2, 3-6, 7-5 and set up a last-eight match against the American Jim Courier, the eighth seed.Reuse content