Sabalenka, who arrived in Miami fresh off a loss in last week's Indian Wells final, wrapped up the first set 6-1 before Romanian Elena-Gabriela Ruse was forced to retire with a right thigh injury.
Up next for three-times Grand Slam champion will be the winner of Saturday's night match between American defending Miami champion Danielle Collins and Swiss qualifier Rebeka Masarova.
Naomi Osaka also won 7-6 3-6 6-4 against American wild card Hailey Baptiste while Italian sixth seed Jasmine Paolini advanced when Ons Jabeur, trailing 4-3 in the opening set, had to retire with a left leg injury.
Osaka, who returned to action in January 2024 after a 15-month break during which she had a baby, said her fitness level was better now than it was in 2021 when she won the most recent of her four Grand Slam titles.
"I feel like I'm better than 2021. You know, COVID really set me back, I'm not going to lie. I was in the house doing nothing," she said.
"But yeah, fitness-wise definitely the best I've been in a couple of years, for sure."
Third seed Coco Gauff also progressed with a 6-2 6-4 win over Greece's Maria Sakkari.
On the men's side, Zverev looked comfortable against British qualifier Fearnley as the German mixed a solid serve with dominance from the baseline while saving the only two break points before winning 6-2 6-4.
For Zverev, who lost at the first hurdle in Indian Wells, the win gave him a German record 145th Masters 1000 win, one more than Tommy Haas. He now faces Australia's Jordan Thompson.
"Happy to kind of have improved a few things from Indian Wells where I didn't feel well on the court. I didn't feel like I played good," Zverev told reporters.
"Hopefully this is just the first of many matches for me here and I can continue playing well."
Meanwhile, Indian Wells champion Jack Draper crashed out, the sixth seed and British number one fell 7-6 7-6 to Czech Jakub Mensik.
Hong Kong wild card Coleman Wong stunned 13th seed Ben Shelton 7-6 2-6 7-6 to advance, while Canada's Denis Shapovalov and American third seed Taylor Fritz also won and will meet in the third round.Â