Holland, who had been restricted to one inning in a B' game because of a sore shoulder, threw 32 pitches, giving up two hits and walking one.
Zunino homered off Rangers relievers Jon Edwards, a solo shot in the fourth with two strikes, and Spencer Patton with a runner aboard in the sixth. Alex Jackson, the Mariners' first-round pick in the 2014 draft, homered in the eighth.
Mitch Moreland hit a two-run homer for the Rangers in the seventh.
Mariners left-hander Roenis Elias allowed two runs - one earned - on five hits and two walks in four-plus innings.