Michael Toglia hit a grand slam and Mickey Moniak also homered in the third inning for the Rockies, who have lost 33 of 43 to Los Angeles.
Ohtani delivered a 448-foot leadoff homer to the back row of the right-field bleachers on the fourth pitch by Germán Márquez (0-3), and the reigning NL MVP added an RBI single that chased Márquez while the Dodgers batted around in the first.
But right-hander Bobby Miller struggled in his Dodgers season debut. The touted prospect who couldn't seize a golden chance to make LA's injury-plagued rotation last season yielded six runs and eight hits in three innings against Colorado, striking out seven.
Toglia interrupted his dismal start to the season with his second career slam in the third, and Moniak added a solo shot four pitches later.
Ben Casparius (1-0) pitched three innings of two-hit relief.
The last-place Rockies went 0-6 on their Southern California road trip, dropping to 3-15 this season.
Key moment
Tanner Scott allowed a single but struck out three Rockies in the ninth for his sixth save. He threw all 11 of his pitches for strikes.
Key stat
Colorado scored more runs than it managed in the first five games of this trip combined (5).
Up next
Yoshinobu Yamamoto (2-1, 1.23 ERA) pitches for the Dodgers at Texas on Friday. Chase Dollander (1-1, 5.06) starts for the Rockies at home against Washington.
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