Gauff sleepwalked through much of the opening set in the first match on Hard Rock Stadium court, but when the alarm went off the US Open champion swept 10 straight games to stun the French lucky loser.
With Gauff pouring on the pressure Dodin began to crumble, piling up nine double faults and 26 unforced errors compared to just seven by her opponent.
"She's a big hitter. She likes the game on her terms," Gauff told reporters. "I was trying my best to get deep in the court and just weather the storm.
"Overall I feel good so far.
"I'm trying to improve with each match. Definitely playing a little bit better than I was last week in Indian Wells."
With the win Gauff matched her best Miami result and will await the winner between Caroline Garcia (30) and Naomi Osaka (26) for a place in the quarter-finals.
After a disappointing day for the American men on Saturday when three of the top four seeds exited, the US women picked up the flag with fifth seed Jessica Pegula (29) and 20th seed Emma Navarro (22) also advancing.
Pegula, who has reached the Miami Open semi-finals for the last two years, took another step towards another appearance in the last four with a 7-5, 6-4 win over Canadian Leylah Fernandez (21).
Navarro, coming off a quarter-final run last week at Indian Wells where she beat world number two Aryna Sabalenka (25) and 17th ranked Elina Svitolina (29), continued her superb form in Miami with a 6-2, 3-6, 6-0 third round win over Italian 12th seed Jasmine Paolini (28).
