Gauff struck a crosscourt backhand long on set point to drop the set.
Serving at 2 all 0-30 in set two, Guaff struck a crosscourt forehand volley long to trail 0-40 before striking a down the line forehand long to drop serve and trail 2-3.
Stephens, the 2017 US Open champion, then held serve at love to lead 4-2.
Serving down 2-4, Gauff double faulted to trail 30-40 in a rollercoaster service game that saw three deuces.
Stephens struck a down the line passing shot winner before Gauff struck a 121 miles per hour down the tee serve which she followed up with netted down the line backhand.
The 28 year old Stephens struck a crosscourt forehand passing shot winner to reach breakpoint three of the game.
Guaff struck an inside out crosscourt forehand wide to drop serve and trail 2-5.
With Stephens serving for the match, the 17 year old Guaff netted two groundstrokes to trail 30-0.
Stephens struck a down the line forehand winner to lead 40-0 and reach match point.
Guaff netted an inside out crosscourt forehand to end the 66 minutes long match.
Stephens, who had converted 3 of 5 breakpoints for the night, gave a fist pump before the two players embraced in a hug at the net.
Gauff, a quarterfinalist at this year's Roland Garros, failed to convert her only breakpoint of the night.
The younger American first rose to fame after defeating Venus Williams in the opening round of Wimbledon in 2019 as a 15 year old.
Stephens next faces the 16th seeded Angelique Kerber of Germany in round three.
Stephens could then face the 3rd seeded Naomi Osaka of Japan in round four.
Osaka takes on the unseeded Leylah Fernandez of Canada in round three tonight at 7:00pm EST USA (4:00pm PST USA) at Arthur Ashe stadium.