Ohtani hit his 31st and 32nd home runs in the third and seventh innings, respectively; Trout hit his 30th long ball in the fifth.
Trout and Ohtani both reached base six times in their nine plate appearances this season, each having six multi-home run performances.
As left-handed starter José Suarez overpowered the Tigers, who dropped the game 7-0.
The Tigers (51-84) finished with four hits and two walks overall. This season, they have been shut out 19 times.
Kody Clemens, a position player, made his third pitching appearance in the previous seven days, pitching the eighth inning.
His first MLB strikeout came against Ohtani with a 68.4 mph eephus pitch, but he also gave up the Angels' 14th, 15th, and 16th hits as well as their 10th run.