Australian Open - Brits: Baltacha, Keothavong through
Baltacha had a tough time at first against the world number 132, who had to qualify for the tournament.
Hampton took the first set after pouncing on Baltacha's service games, and came within a couple of games of the match as the second set went to 4-4 on serve.
But Baltacha dug deep, scooping the set and seizing the momentum with an early break in the third.
Hampton of the United States clawed that back, but could not do so a second time as Baltacha struck again.
"She was out there and she had nothing to lose," Baltacha said. "She was just swinging.
"She played a really good match. I remember that from being a qualifier. You feel you’ve earned your spot and you have nothing to lose.
"I kind of thought, 'No, you know what, I'm main draw here. I've worked very hard. I had an unbelievable year. I'm going to keep it together'.”
Next up for Baltacha will be a tough clash against last year's beaten finalist Justine Henin, seeded 11 in Melbourne this year.
“She's one of the legends," the 27-year-old said of the Belgian. "I think it's going to be more about myself trying to control what I can control and just trying to really deliver.
"I've got to go out there and I've really got to believe that I can beat her, because, like I said, there would be no point. It would be like a walk in the park for her.”
Keothavong's route was more straightforward, and having impressed with three straight-sets wins in qualifying, the world number 118 continued her run to beat Russian Rodionova and reach the second round in Melbourne for the first time.