"I feel like I can play even better, which is what's more exciting," Gauff told the WTA website after the match on Sunday.
Sebastian Baez put Argentina ahead when he defeated world No. 6 Taylor Fritz, which was also his second win against a Top 10 player.
However, Gauff ensured the US began its winning run in the mixed team event in Perth.
She defeated Solana Sierra and then, along with Harrison, recorded a convincing 6-4, 6-1 victory over Maria Lourdes Carle/Guido Andreozzi.
Gauff/Harrison dominated the match. They dominated the exchanges from the baseline and were sharper at the net to win after 63 minutes.
The US now leads 1-0 in Group A and next faces Spain.
