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.
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."
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
14°C