But the defensive-minded Halep, who at times reached down to rub a troublesome right ankle, improved as a match lasting over two hours wore on, getting the better of Dodin in extended rallies and in the key moments of the match.
The turning-point came when Halep had break points at 5-5 in the third set and jumped all over a weak second serve from the 21-year-old Dodin to move ahead.
Halep won the next game to love, rocketing down an ace on match point to set up a meeting with 30th-seeded Pole Agnieszka Radwanska who defeated Belgian Alison Van Uytvanck 6-3 7-6(4).
Halep has amassed enough ranking points that her number one standing is not in jeopardy in Miami. She would have maintained top spot even if she had lost on Thursday and world number two Caroline Wozniacki went on to win the tournament.
Angelique Kerber, the 10th seed, cruised to a 6-2 6-2 win over Swede Johanna Larsson, setting up a third-round showdown with Russian 23rd seed Anastasia Pavlyuchenkova.
Fifth-seeded Czech Karolina Pliskova dispatched Russian Ekaterina Makarova 7-5 7-5 and unseeded German Carina Witthoft upset her 12th-seeded countrywoman Julia Gorges 7-6(2) 4-6 6-4.
