Ohtani's two run shot came off Red Sox closing pitcher Matt Barnes and snapped a four-game losing skid for the Angels.
"Coming off a losing streak and the first two games of the series, the way we lost, it wasn't a good way to lose," Ohtani said. "So, it was huge for us and the team to come up with this. We showed that we can beat any team."
Mike Trout hit a bloop single after Barnes had retired the first two batters he faced in the ninth as the Angels tried to avoid a three-game sweep to Boston.
Trout, who had no hits in his last 18 bat appearances, hit his single to right center field. Ohtani came up next and hammered the first pitch, a 96 mph fastball, to right field.
It was Ohtani's 12th home run of the season and it came against Boston's ace closer Barnes, who was nine-of-nine in save opportunities this season.
"He's the most physically gifted baseball player that we've ever seen," Barnes said. "I don't know that you're ever going to see someone who can throw 100, 101 and hit the ball 600 feet. He's a special player and incredibly talented. Hopefully, he stays healthy and has a long career."
Mike Mayers earned his second save of the season for the Angels by striking out three batters in the ninth.
The Angels jumped to a 4-0 lead in the second off Red Sox starter Nathan Eovaldi, getting four hits, a hit-batter and a walk in the inning.