The only highlight for the Angels, who have lost five of six, came when Ohtani led off the game with a homer, his MLB-leading 41st.
Baltimore won two games in a row for the first time since July 30-31 and took its first series since a three-game sweep of Washington from July 23-25.
The Orioles hit three home runs off Ohtani a night earlier, although the two-way star left the mound with the lead.
Keegan Akin (1-8) earned his second career victory, pitching seven innings and allowing one run on three hits with six strikeouts and two walks. When Akin pitched as a starter or out of the bullpen for Baltimore, the team had lost its previous 12 games.
When Severino smacked reliever Jake Petricka's first ball into the centre-field bullpen in the fifth inning, the Orioles were up 3-1. It was Severino's second career grand slam and the team's third this season.
Severino added a two-run single in the eighth to score Baltimore's final two runs. His six RBIs were a career-high.
Orioles rookie Ryan Mountcastle went 2 for 4 with a walk and added a two-run single in eighth, extending his on-base streak to a season-high 17 games. Ramón Urias had three hits and two RBIs.
Ohtani hit a towering blast over the right-field wall on the game's second pitch, his third leadoff homer this season.
The Orioles tied the game in the third on a run-scoring single by Kelvin Gutierrez that scored Jahmai Jones, who doubled off starter Jaime Barria.
In the fifth inning, Trey Mancini's RBI single bounced out of the infield, giving the Orioles a 2-1 lead. DJ Stewart followed with a two-run home drive.
With inputs from the Associated Press