Ohtani led off the game with a homer, his MLB-leading 41st, but that was the only highlight for the Angels, who have lost five of six.
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 homers off Ohtani a night earlier, although the two-way star left the mound with the lead.
"It was kind of emotional last night and to follow it up with a nice win today, it's a good feeling," Orioles manager Brandon Hyde said.
Keegan Akin (1-8) picked up his second career win, allowing one run and three hits with six strikeouts and two walks over a season-high seven innings.
"That's what you dream of as a starting pitcher," Akin said. "You want to go out there and go six, seven, eight innings almost every outing. Obviously, it's a lot harder to do that than it is to say to do it. It's a great feeling and good to finally get a series win."
Baltimore had lost its last 12 games when Akin appeared as a starter or out of the bullpen.
The Orioles led 3-1 in the fifth when Severino hammered reliever Jake Petricka's first pitch into the center-field bullpen. It was the second career grand slam for Severino and third for the team this season.
"We had a tough moment losing (19) games in a row, we didn't play right and I just tried to help the team win," Severino said. "I just got the bases loaded there and tried to put my barrel on it and I got a good result."
Elvis Peguero (0-1) was charged with five of the six runs the Angels allowed in the inning.
Severino added a two-run single in the eighth to score Baltimore's final two runs. His six RBI were a career high.
"Once they hit the grand slam, it became not such a good game," Angels manager Joe Maddon said. "Up to that point, I had no issues whatsoever. You have to consider it's the last game of a baseball-grueling road trip. We have a lot of issues with the bullpen and pitching in general."
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 RBI.
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.
The Orioles took a 2-1 lead in the fifth on an RBI single by Trey Mancini that bounced out of the infield. DJ Stewart followed with a run-scoring double.
"I thought that Keegan helped us stay in the game and allowed us to put that rally together," Hyde said.
Angels: OF Justin Upton did not start for a third consecutive game because of a left calf injury.
Orioles: OF Jorge Mateo did not play because of soreness in his lower back.
Angels: Maddon has not announced a starter for the opener of a series against the Padres on Friday. "There's a lot of different options available to use," he said.
Orioles: Matt Harvey (6-13, 6.27 ERA) gets his 26th start of the season Friday against the Tampa Bay Rays. He's allowed 14 earned runs and 23 hits over 19 innings over his last four appearances, after throwing 18 1/3 scoreless innings over three starts coming out of the All-Star break.
Ohtani cranks his 41st HR of the season
Shohei Ohtani hits a solo shot deep to right field as the Angels lead the Orioles 1-0.