Not that the 13th seed was too impressed by her Independence Day display on a sunny Court Three.
"It was an incredibly tough match but I kept fighting," the 23-year-old, one of five American women to reach the third round, said on court. "I think the quality wasn't that great today but I will hit the practice courts tomorrow."
Anisimova, a quarter-finalist in 2022, secured the decisive break of serve in the first set with a stunning lob to lead 5-3.
She had chances near the end of the second set too but was pegged back as 110th-ranked Galfi dug deep to break serve at 5-6 and set up a decider.
Anisimova let out a big scream as she broke serve early in the third set with a wrong-footing forehand and an even louder one when she saved a break point when leading 3-2.
Another break of serve put Anisimova in complete control but at 5-2 she double-faulted on break point down to give Galfi hope. But it did not prove costly for the American who sealed the win a game later to move through.