Rain delayed the start of the match but once play began Gauff needed only 53 minutes to see off her French rival. The 19-year-old has not dropped a set in her title defence and did not face a single break point on Friday.
The world number three raced through the opening set and took a 4-0 lead in the second before Gracheva held serve, and with dark clouds gathering once again Gauff was quick to wrap up a victory which pits her against Emma Navarro in an all-American semi-final.
"I was focusing on playing my game," Gauff said.
"I thought I served really well, probably the best so far in the tournament, which is something I've been working on off-season. I'm really happy with how I played.
"I'm glad I was able to finish my match (before it could rain)."
At the Brisbane International, another warm-up tournament for the Australian Open, world number two Aryna Sabalenka overcame Daria Kasatkina 6-1, 6-4 to set up a semi-final clash with Victoria Azarenka.
Sabalenka stormed through the first set but faced a stiffer challenge in the second as Kasatkina raised her game even though she could not force a decider.
Defending Australia Open champion Sabalenka fired 29 winners, compared to seven by her opponent, to snuff out Kasatkina's hopes of a comeback.
"It's hard there because you get to know each other better and better every time you play," Sabalenka, who now has a 6-2 head-to-head lead against Kasatkina, said of their rivalry.
"It's always tough. She's really a great player, a great fight... Going into this match, I knew there's going to be a hard battle and I have to be ready."
She will meet Azarenka, who outlasted Jelena Ostapenko 6-3, 3-6, 7-5 to make the last four. Ostapenko came from one set down to stretch the match into a decider but Azarenka had the last laugh in the thrilling three-setter.
Elena Rybakina reached the last four after her opponent Anastasia Potapova retired through injury after losing the first set 6-1. She will meet Linda Noskova, who beat Mirra Andreeva 7-5, 6-3, in the other semi-final.
