Baltimore improved to 6-1 on its nine-game road trip. The Orioles (89-51) are 47-25 on the road this season, the best mark in the American League.
Gunnar Henderson had three hits for Baltimore, and Aaron Hicks had two hits and two RBIs. O'Hearn and Rutschman each contributed two hits and two runs, and Rutschman knocked in three.
O'Hearn opened the scoring when he belted a solo home run off Boston starter Tanner Houck (4-9) in the fourth inning. It was O'Hearn's 12th of the season.
Rutschman's 18th home run was a solo shot against reliever John Schreiber that made it 6-2 in the eighth.
Baltimore starter Kyle Bradish (11-6) struck out nine in six innings. He gave up two runs on four hits and didn't walk a batter.
The Orioles, who lead the American League East, took control of the game by scoring four runs in the sixth. The victory allowed Baltimore to maintain its four-game lead over the Tampa Bay Rays (86-56), who beat the Seattle Mariners 7-4 on Friday.
Connor Wong hit a solo home run for the Red Sox, who have lost three in a row. Boston (72-69) has lost its past five home games.
Houck (4-9) allowed five on eight hits in 5 1/3 innings. He struck out five and walked two.
Baltimore's four-run sixth included a double by Cedric Mullins that drove in two for a 3-0 lead. Austin Hays followed with a single that knocked in Mullins to make it 4-0, and then Rutschman subsequently pushed the lead to 5-0 when his sacrifice fly drove in Hays.
The Red Sox scored twice in the bottom of the sixth. After Wong's ninth home run of the year, Alex Verdugo doubled and scored on Justin Turner's two-out double.
Following Rutschman's homer in the eighth, Baltimore increased its lead to 7-2 when Henderson tripled and scored on Brennan Bernardino's wild pitch. The Orioles tacked on four runs in the ninth.
—Field Level Media