In a showcase between two players among a promising group of emerging US women, 15th seed Stephens used a combination of bigger groundstrokes and more accurate serves to charge past an error-prone Hampton in 63 minutes.
"I just tried to play my best. It's tough playing Jamie, a good friend. Definitely a tough match to come out here on Ashe," said 20-year-old Stephens. "I just tried to stay focused and do my best and luckily got the 'W'."
Stephens, who burst into the international spotlight by upsetting Serena Williams in the quarter-finals of the Australian Open and reached the last eight at Wimbledon, benefitted from 34 unforced errors from Hampton.
Stephens, who also reached the fourth round at Roland Garros for the second successive year, put 70 percent of her first serves into play, while Hampton found the range on less than half of her first deliveries, putting her on the defensive.
Hampton, ranked 26th, broke serve in the sixth game of the second set to put it back on serve at 3-3, but at 30-30 in the next game she missed a backhand overhead volley and Stephens broke her one point later and did not lose another game.
Hampton, 23, had enjoyed an impressive stretch on tour, beating two seeded players at the French Open including 2011 Wimbledon champion Petra Kvitova to reach the fourth round. She made it to the Eastbourne final on grass and the semi-finals on the hard courts of Stanford.
The Americans had last played in the first round at Wimbledon, with Stephens winning 6-3 6-3.
Next up for Stephens could be another all-American clash as she faces either defending champion Williams or Yaroslava Shvedova of Kazakhstan.
Stephens said her approach going forward would remain simple.
"Just play my best, play my game," she said. "All you can do is do your best and that's what I'm going to count on."
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- Serena Williams