Keys broke Russian Potapova's serve for a third time to clinch the first set and rolled through the one-sided second set under sunny skies in the California desert to extend her winning streak to 13 matches.
"I'm so happy to be here," Keys said in an interview on center court after the match.
"Australia was obviously an amazing moment so it's really nice to be playing at home for my first tournament back at a place I've played at so many times in front of some amazing people."
Next up for world number five Keys is a third-round meeting with either 28th seed Elise Mertens or Kimberly Birrell of Australia, who play later on Saturday.
Californian Fritz, who lifted the trophy here three years ago, struggled to reach the finish line against Italian Matteo Gigante but ultimately prevailed 6-3 7-5 in front of a full house on Stadium Two court.
Fritz was unable to serve out the match at 5-4 in the second set but broke back in the next game en route to the finish.
The third seed said he was being patient with himself as he was coming off an abdominal injury he suffered right after the Australian Open that kept him out of the tournament in Acapulco last month.
"There's definitely things I could have done better in the match but overall it was a pretty solid match," he said.
"I can't expect to come back and play perfect tennis. I've been injured, so I didn't have ideal prep coming into the tournament."
Fritz will face 30th-seeded Chilean Alejandro Tabilo for a spot in the round of 16.