Ohtani, starting for the first time since May 20th, allowed one run ond three hits in five innings. He walked three and struck out five while throwing 83 pitches.
Tigers starter Mike Fiers was also knocked out by the second rain delay in the top of the sixth, allowing one run and seven hits in 5 2/3 innings.
The Tigers quickly took the lead in the bottom of the sixth, loading the bases against Cam Bedrosian (1-1) on a single, a walk and a hit by pitch. Greyson Greiner struck out, but Iglesias lined a two-run single to center to put Detroit ahead 3-1. Dixon Machado grounded to short, but Andrelton Simmons' throw to the plate was too late to get JaCoby Jones.
Leonys Martin and Nicholas Castellanos followed with RBI singles off Jim Johnson to push the lead to 6-1.
Louis Coleman (2-0) got the win with 1 1/3 innings of relief.
Ohtani looked rusty in the first inning, walking two of the first four batters he faced before allowing Niko Goodrum's two-out RBI single.
The Angels tied it in the third when Albert Pujols' two-out single drove in Mike Trout.
Ohtani, who was throwing 91-mph fastballs in the first inning, hit 98 on his final pitch of the third to retire Victor Martinez on a soft liner to shortstop.
The game was delayed for 23 minutes by rain at the end of the fourth inning, but both starters stayed in the game.
Ohtani walked Martin with two out in the fifth and allowed a double to Castellanos before getting Jeimer Candelario to ground out on a 101-mph fastball.
The game was delayed again by rain in the top of the sixth, this time for 41 minutes. Coleman replaced Fiers to get the last strike of the sixth, and Bedrosian came in for Ohtani.
A Canada Goose settled into right-center field during the second rain delay, and an attempt to remove it ended in chaos. After the grounds crew set off two firecrackers and another member gave chase, the bird tried to escape, but crashed into an LED board on the façade of the third deck and fell two levels into the stands.
After several moments, a veterinarian who was attending the game wrapped the stunned goose in a blanket and took it to the concourse, where it was released outside the stadium and dashed into nearby bushes.
Angels: Zack Cozart (forearm tightness) was a late scratch from the Angels' lineup.
Tigers: Detroit put LHPs Francisco Liriano (right hamstring strain) and Daniel Stumpf (ulnar nerve irritation) on the 10-day DL. Liriano's move is retroactive to Sunday, Stumpf's to Tuesday. The Tigers recalled RHP Johnny Barbato and LHP Ryan Carpenter from Triple-A Toledo. ... Iglesias left the game after the sixth with a hip contusion.
Carpenter (0-1) starts for the Tigers on Thursday against Angels LHP Andrew Heaney (2-3) in the finale of the four-game series.